The match started on high note as Raheem Sterling gave City a one nil lead in the fourth minute but four minutes later Spurs were leading 2-1 courtesy of Son Heung-min two goals.
City were back on level through Bernado Silva's deflected shot and Raheem Sterling put them ahead in the 20th minute. Sergio Aguero's second half goal appeared to have sealed City's fate but there was still more drama as Fernando Llorente goal was confirmed by VAR.
City appeared to have scored the winning goal through Sterling but the the goal was ruled offside by VAR as Spurs matched to semi finals on away goal rule.
There were four minutes to go before half-time when Mauricio Pochettino made one of the boldest calls of his managerial career. Moussa Sissoko, a strong-running midfielder, limped slowly from the pitch; Fernando Llorente came on.
Tottenham were still going through, at the time, but Pochettino did not favour caution. He had plenty of defensive cover on the bench. He chose to introduce a striker, tinker with the team shape. Some 32 minutes later, Llorente would score the goal that sent Tottenham through to the Champions League semi-final. Fortune favours the brave; or, to dare is to do, as they like to say in that part of north London
Elsewhere, Liverpool booked a semi final date with Barcelona as they beat Porto 4-1 to win 6-1 on aggregate.