It seemed Mauricio Pochettino's Tottenham side had blown any chance of reeling in Chelsea when they trailed Swansea City 1-0 in the 88th minute on Wednesday.
Courtois continued to be increasingly influential as the game went on, including making a courageous stop from Aguero in injury time to help secure the victory after Eden Hazard had scored his, and Chelsea's, second goal.
An 11th consecutive home league victory in the lunchtime kickoff would cut Chelsea's lead to four points before Antonio Conte's side play away at Bournemouth in the day's late game.
But Courtois made amends, producing a fine save to deny Leroy Sane and give everyone in blue a vital lift in the process.
Pep Guardiola's City, for all their slick inter-play, are now looking anxiously over their shoulders at Arsenal and Manchester United after four games without a win.
He said: "Rio may think differently as he's had different experiences to me".
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"I liked the way they played when we were there, now they play with a lot of talent - not just long balls, a lot of quality".
"It is something you need as an individual and as a side when you're trying to win the title". The Tottenham result is important but the most important results is ours, we have to continue to think like that.
Chelsea's Diego Costa will not face retrospective Football Association action after appearing to kick out at Manchester City captain Vincent Kompany. It was 1-1 all of a sudden but I had to remain focused. "I saw many teams play here with six at the back".
"Our performance was 1 000 miles better than the Arsenal game".
"We are almost there but there is a long way to go. Usually I like to say only who wins write the history".
But Gerrard still thinks we're in a better position than rivals Arsenal and Manchester United, who now sit in fifth and sixth respectively. Tottenham looked set for a defeat that would have killed off their hopes until they produced three goals in the final stages of the game at the Liberty Stadium.
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