Diego Costa's late header defeated AC Milan and put Atletico Madrid on course for a first Champions League quarter-final since 1997.
Costa powered home at the back post to beat a Milan side that earlier had the better chances.
Visiting goalkeeper Thibaut Courtois tipped on to the woodwork from Kaka and Andrea Poli respectively.
Raul Garcia, who blazed over, looked to have wasted Atletico's best opportunity before Costa's intervention.
Milan battle history
•Only two sides have won a Champions League knockout tie of any round after losing a home first leg. Ajax beat Panathinaikos in the 1995-96 semi-finals and Inter Milan defeated Bayern Munich in the 2010-11 round of 16.
From a corner on the Atletico right, Milan defender Ignazio Abate's attempted clearance travelled almost straight up into the air.
Costa, back-pedalling, superbly generated enough power on the dropping ball to beat scrambling home goalkeeper Christian Abbiati.
With that, Milan coach Clarence Seedorf was consigned to defeat on his managerial debut in a competition he won four times as a player.
He would have earlier been encouraged by an energetic Rossoneri display far removed from the domestic struggles that sees them lie ninth in Serie A.
On his Champions League bow, Adel Taarabt, on loan from QPR, grew in confidence on the Milan right, while Kaka showed glimpses of the ability that saw him crowned world player of the year in 2007 - the last time Milan lifted the Champions League trophy.
After a bright Atletico start, Milan warmed to their task, with a move down the right involving Taarabt eventually feeding Kaka.
The Brazilian's curling shot from the corner of the box was deflected, before the flying Courtois finger-tipped the ball on to the bar.
Soon after, the Belgian on loan from Chelsea was forced into another, even better, save. This time, Taarabt's cross found Poli six yards out, with the header pushed on to the post.
Fifth-time success
•Atletico's victory is their first European Cup knockout win in the Champions League era. In four previous games they had drawn three and lost one.
More chances would come for the home side - Kaka curling on to the roof of the net from a Mario Balotelli backheel, before the former Manchester City man fired narrowly wide from distance.
Still, it was to Courtois that Atletico were indebted, the Spanish side only managing weak headers from Costa and Garcia in the first period.
Atletico, though, were one of only three unbeaten teams during the group stage and have the confidence of a side level on points with Real Madrid and Barcelona at the top of La Liga. As Milan tired, Diego Simeone's men came to the fore.
Gradually pressing Milan back, Los Rojiblancos could have taken the lead when Garcia was found on the edge of the six-yard box, only for his shot to fly high over the bar.
A goalless opening leg loomed, but that was to discount 25-year-old Costa's decisive contribution eight minutes from the full-time whistle.
There was still time for Adil Rami to drive from distance, but with his effort travelling wide, Milan were beaten and pushed towards a fifth successive knockout defeat at the hands of Spanish opponents.
Diego Simeone believes Atletico Madrid played an 'intelligent game' as they edged out AC Milan at the San Siro.
The La Liga outfit found themselves on the back foot for much of the first half, with only Thibaut Courtois and the woodwork standing between Milan and a commanding lead.
Atletico grew into the game, though, and netted late on through Diego Costa to ensure that they head home with a narrow lead to defend in the return leg of their UEFA Champions League last-16 encounter.
Simeone believes they are deserving of such a standing, with their performance levels having improved as the night progressed.
"We kept ourselves in the game and the goal we scored allowed us to get the result we were hoping for."
He told Sky Italia: "We knew we were going to face an intense Milan side, especially in the first half.
"In the first half we lost too many balls in midfield and suffered a little. We didn't play with the right tempo.
"In the second half we changed, we blocked (Mario) Balotelli and Kaka better and we started to control midfield.
"We kept ourselves in the game and the goal we scored allowed us to get the result we were hoping for.
"We took advantage of the moment we created. I think in the second half we played an intelligent game."
Atletico are taking nothing for granted, though, with match-winner Costa aware that only half of the job has been completed.
He said on UEFA's official website: "We know that this is not finished yet. We have a good result but Milan are a great side and anything can happen. We are not going to be over-confident.
"After our (recent run) of defeats people lost faith in us but we have since shown how strong we are."
Borussia Dortmund took a giant stride towards the Champions League quarter-finals with a comfortable last-16 first-leg win at Zenit St Petersburg.
Dortmund made a rapid start as Henrikh Mkhitaryan swept in a loose ball after a dangerous run from Marco Reus, who cracked in a second 77 seconds later.
Oleg Shatov's low second-half shot gave Zenit hope, before Robert Lewandowski drilled in Dortmund's third.
Hulk's vicious penalty reduced the gap, only for Lewandowski to pounce again.
The Poland striker, who will move to Dortmund's arch rivals Bayern Munich in the summer, ensured the German side have a healthy - and fully deserved - two-goal advantage heading into next month's second leg.
Dortmund, who were beaten by Bayern in last season's Champions League final at Wembley, dominated their Russian hosts as they put their domestic woes to one side in a ruthless attacking display.
Jurgen Klopp's team have struggled in the Bundesliga this season, with the weekend's 3-0 defeat at lowly Hamburg leaving them 20 points adrift of leaders Bayern.
But they have fared much better on the European stage, progressing into the knockout stage from a tricky group containing Premier League title chasers Arsenal, big-spending Italian side Napoli and French runners-up Marseille.
Dortmund looked intent on making amends for their Bundesliga troubles and constantly threatened to hurt Zenit with swift and penetrating counter-attacks.
They were helped by some rusty defending from the home team, who had not played a competitive fixture since 11 December because of the mid-season Russian break.
Dortmund in Europe
Dortmund are competing in the Champions League knockout phase for two successive seasons for the first time since managing three in a row between 1995-96 and 1997-98. Then, under Ottmar Hitzfeld, they lifted the trophy in the second season.
The Russian leaders allowed Germany international Reus to weave into their penalty area and, despite being fouled by two home defenders, he stayed on his feet to feed Mkhitaryan for the opening goal.
Reus doubled the lead after collecting Kevin Grosskreutz's pass as Dortmund threatened to run riot in a devastating opening burst.
But Zenit managed to regroup after half-time and reduced the arrears following a chaotic scramble inside the Dortmund box. Venezuelan debutant Jose Rondon, who appeared to be in an offside position, hit the post before Oleg Shatov rifled in the loose ball.
The comeback lasted for only three minutes before Lewandowski combined with Poland team-mate Lukasz Piszczek to drill through the legs of Zenit goalkeeper Yuri Lodygin from 12 yards.
Zenit were given another lifeline when Scottish referee William Collum harshly adjudged that Piszczek had brought down Viktor Fayzulin. Brazil striker Hulk, who had missed his previous three penalties, thumped an unstoppable effort into the top right corner.
However, their defence switched off almost straight from the restart and Lewandowski drove in a fourth goal for the visitors to make their task in the return leg on 19 March look more straightforward.
Lineup, Bookings (3) & Substitutions (6) Zenit St Petersburg
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