The extra 30 minutes failed to produce more goals, pushing the game to penalties.
Tottenham Hotspur defeated Atletico Madrid 3-2 but exited the UEFA Champions League after a 7-5 aggregate loss in their last-16 tie.
Liverpool found an opportunity to level the score within 90 seconds of the second half.
With Burnley’s persistent efforts, they managed their first goal against City in nine games during stoppage time.
Just before the halftime break, Nathan Ake restored the hosts’ lead.
Argentina will face the winner of tomorrow’s semi-final game between France and Morocco for a place in the final of the World Cup on Sunday.
The Reds came for a revenge having lost last season’s Premier League title to City.
