The France striker opened the scoring against Rostov with a brilliant flick, but Sardar Azmoun equalised – only the fourth time in 19 home Champions League games under Diego Simeone that Atletico have conceded – before Griezmann fired in off the crossbar in injury time.
Bayern won 2-1 at PSV, with Poland striker Robert Lewandowski scoring twice and hitting the woodwork three times – taking his tally for club and country this season to 19 goals in 17 games.
Paris St-Germain also went through thanks to a 2-1 victory at Basel.
Thomas Meunier scored a brilliant late volley for the French champions, who qualified with Arsenal from Group A.
A draw would have been sufficient for Unai Emery’s PSG side thanks to Arsenal’s 3-2 win at Ludogorets.
Napoli missed the opportunity to clinch their last-16 place as they drew 1-1 at Besiktas.
Ricardo Quaresma gave the Turkish champions a 78th-minute lead before Marek Hamsik curled home a fantastic 25-yard effort four minutes later.
Benfica beat Dynamo Kiev 1-0 courtesy of Eduardo Salvio’s 45th-minute penalty.
Who could go through on Wednesday?
Borussia Dortmund will progress if they beat Sporting Lisbon at home. Real Madrid will join them from Group F if they win at Legia Warsaw, providing Dortmund win.
Leicester will go through if they beat FC Copenhagen at the King Power Stadium. A draw would be enough for the Foxes if FC Porto do not beat Club Brugge.
Victory over Lyon will secure Juventus’ place in the last 16, which would mean Sevilla will qualify if they beat Dinamo Zagreb.