Simeone's men had beaten Bayern Munich, PSV Eindhoven and Rostov 1-0 but Tuesday's dramatic late win over the Russians was the closest they have come to dropping points, needing a 94th minute Antoine Griezmann goal to snatch victory.
The Frenchman, who opened the scoring just before the half-hour mark to end a run of five games without a goal before Azmoun quickly equalised, thought his winner had been ruled out for offside and had to wait before wildly celebrating.
"In Atletico we always appreciate these types of wins," said defender Filipe Luis. "It often happens.
"At home we want to win every game 3-0 or 4-0 but sometimes teams close up shop and it's tough. This is the Champions League, and we've proved we're in the top 16 teams in Europe."
Atletico have evolved from being built on defence and counter-attacks to a fluid, complete team with an ability to hammer opponents, demonstrated in La Liga by a 7-1 victory over Granada in mid-October and Saturday's 4-2 win against Malaga.
They have also retained a knack for winning testing games by the tightest of margins, particularly in the Champions League, where they have beaten all of their opponents a solitary goal.
"We have more alternatives this season," said midfielder Koke, who has taken a more central role after being used on the left wing in previous campaigns. "We were hard to predict last season too, but now we are even more varied."
Atletico top the group on 12 points with two games remaining and will battle it out with Bayern, who have nine, for top spot and seeded status in the last 16 draw. They host PSV on Nov. 23, and visit Bayern, who they beat in September, on Dec. 6.
(Reporting by Richard Martin; editing by Ken Ferris)
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