Alexis Sanchez scored a dramatic extra-time winner as Arsenal came from behind to beat Manchester City 2-1 in the FA Cup semi-final at Wembley.

The Chile international struck from inside the six-yard box in the first period of extra-time as the Gunners booked a final date against London rival Chelsea.

In a controversial match, Sergio Aguero had a penalty appeal turned down and a goal disallowed by referee Craig Pawson, who also rejected Sanchez's demands for a first-half spot-kick.

City striker Aguero did score for the 12th time in as many games to put City ahead just after the hour mark, but Nacho Monreal hit back with his first goal in over two years.

Yaya Toure and Fernandinho both hit the woodwork for City as the match moved into extra-time, where Sanchez's strike proved decisive.

Arsene Wenger is under intense pressure with his Arsenal contract due to expire in June, but he now has the chance to win his seventh FA Cup, which would give him the outright record, following up on his side's 2014 and 2015 triumphs.

City had won its past eight FA Cup semi-final appearances, but this defeat means that, despite huge expectations upon his arrival, Pep Guardiola is almost certain to finish a managerial campaign without a trophy for the first time in his career.

Guardiola's focus must immediately switch to ensuring his side can at least salvage a top-four Premier League finish, with a crucial derby against Manchester United coming up on Friday (AEST).