Antoine Griezmann added a 93rd-minute winner to his excellent earlier effort as Atlético broke Rostov's impressive resistance to preserve their 100% start to the campaign.
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Antoine Griezmann's stoppage-time goal snatched all three points as Atlético preserved their 100% start to the UEFA Champions League and booked a place in the knockout stage.
It was the second of the game for Griezmann, who had dexterously broken the deadlock against the run of play on 28 minutes, hooking the ball past Soslan Dzhanaev.
The lead lasted two minutes as Rostov managed to do what Bayern and Barcelona had both failed to do this season – score at the Vicente Caldéron. Dmitri Poloz broke at pace and timed his pass to Sardar Azmoun perfectly. The finish was unerring.
Following a stern talking-to from coach Diego Simeone at half-time, Atlético spent much of the second period on the front foot. Rostov held on brilliantly, though, and seemed set for an unlikely point until Griezmann popped up at the death.
Key player: Antonie Griezmann (Atlético)
The Frenchman was anonymous for large parts of this Group D contest, but showed just how important he is to the Spanish capital outfit with two exceptionally taken goals in what was a finishing masterclass. Atlético were unable to create too many chances against a dogged Rostov side, yet thankfully for them Griezmann was excellent when required to be. Isn't he always?
Atlético's champion spirit
They say it is the mark of champions when you win without playing well. If that is the case then you wouldn't bet against Atlético lifting the trophy come June. After being pegged back to 1-1, the hosts were frustrated and stifled by Ivan Daniliants' 5-3-2 system and restricted to speculative efforts until deep into injury time Griezmann then popped up with a winner. It could be a big goal in the club's quest for European glory.
So near yet so far for Rostov
Playing in the UEFA Champions League is all about fine margins and a bit of luck. This has been a steep learning curve for Rostov and had they held on for a point, it would have been thoroughly deserved. Largely subdued for most of the evening, Griezmann showed why he is one of the game's top forwards with two superb goals. He was the difference between the teams.
Joe Walker, Atlético (@UEFAcomJoeW)
What a finish! Rostov were Atlético's equals here tonight and that is a big compliment given the Rojiblancos' European record. The home side huffed and puffed and never looked like blowing the house down, but somehow they did – just about. It was harsh on the visitors, but Simeone will not care one jot. Four wins from four and a place in the last 16 secured.
Richard van Poortvliet, Rostov (@UEFAcomRichVP)
A desperately disappointing result for Rostov, who certainly merited a point against one of the best teams in Europe. When the dust settles, Rostov can take a lot of heart from their performance. Defensively they were solid and they also created a number of opportunities. This is a side that are improving with every matchday and PSV Eindhoven have a battle on their hands for third and a UEFA Europa League spot.