Alexis Sanchez's scrambled extra-time winner secured Arsenal an FA Cup final date with Chelsea - and ensured Manchester City manager Pep Guardiola will end a season without a trophy for the first time in his coaching career.
Sanchez settled a contentious semi-final 11 minutes into the extra period after Manchester City failed to clear Mesut Ozil's free-kick.
Arsenal showed great resilience to come from behind - and eased the pressure on manager Arsene Wenger - after Sergio Aguero raced clear of Nacho Monreal to put City ahead in the 62nd minute.
Monreal made amends with the equaliser 11 minutes later as he drilled in Alex Oxlade-Chamberlain's cross at the far post - but City were left nursing a serious sense of injustice after this disappointing defeat.
They had a goal wrongly ruled out in the first half when Leroy Sane's cross was adjudged to have gone out before Aguero and Raheem Sterling combined to turn it into the net, while Yaya Toure and Fernandinho hit the woodwork after the break.
It left Arsenal victorious and Wenger aiming for a record seventh FA Cup triumph.
Victory in the final on 27 May would strengthen his and Arsenal's case for continuity, but for now there was much for the Frenchman and his players to treasure about this triumph.
Manchester City will argue long and hard that their chances of reaching the final were sabotaged by a first-half decision that saw a good goal ruled out.
Referee's assistant Steve Child judged that Sane's cross had gone behind before Aguero turned it back at the far post and then Sterling made sure. Replays suggested the ball had not gone out and City were the victims of an injustice.
City will also feel Lady Luck deserted them as they lost playmaker David Silva to injury early on and saw those efforts from Toure and Fernandinho hit the woodwork.
In the final reckoning, they must also accept the brutal truth that once more they enjoyed superiority in possession and territory but could not find the ruthless touch.
Arsenal - the key match stats
Arsenal have reached their 20th FA Cup final, a competition record.
This was Manchester City's first FA Cup semi-final defeat since 1932, also against Arsenal - the Citizens had won eight consecutively before this defeat.
Alexis Sanchez is Arsenal's top scorer in games at Wembley, with four goals - he overtook Marc Overmars and Ian Wright on three.
Sanchez has now been involved in more goals than any other Premier League player in all competitions this season (38, 24 goals and 14 assists).
Sergio Aguero has scored 12 goals in his past 12 matches for Manchester City in all competitions.
It was Aguero's second goal at Wembley, having netted for City against Chelsea in the FA Cup semi-final in April 2013.
Nacho Monreal's last two goals for Arsenal have come in the FA Cup, both against Manchester clubs (having scored against Manchester United in March 2015).
Alex Oxlade-Chamberlain has six assists in his past 10 FA Cup starts for Arsenal. In all competitions this season, only Mesut Ozil (10) and Alexis Sanchez (14) have more assists than Oxlade-Chamberlain (nine).