Silva strikes late as Man City sink Chelsea to reach FA Cup final
Pep Guardiola's side were second best for long periods of the semi-final, but Chelsea wasted a string of chances before Silva delivered the knockout blow six minutes from full-time.
Shaken by their Champions League quarter-final loss against Real Madrid on penalties in midweek, City took a while to shake off the gloom from the end of their treble bid.
They were hampered by the absence of Norway striker Erling Haaland after he suffered a knock against Real, with Julian Alvarez unable to make an impact as his replacement.
City were bailed out by Chelsea striker Nicolas Jackson's profligacy and Guardiola will hope the hard-fought success provides a timely lift as they chase a Premier League and FA Cup double.
City face Manchester United or Coventry, who meet on Sunday, in the final on May 25 and will retain the Premier League title if they win their last six games.
It will be City's 13th final in the competition and potentially a repeat of last year's 2-1 win over United in the Wembley Manchester derby.
Beaten by Liverpool in the League Cup final in February, Chelsea's wait to win their first domestic trophy since the 2018 FA Cup goes on for another season.
It was a bitter blow for Blues boss Mauricio Pochettino, who has endured a difficult first season in charge and remains without silverware in England.
The semi-final was billed as in-form Chelsea forward Cole Palmer's chance to punish his old club for selling him to the Blues in September.
Guardiola said Palmer was asking to leave City for two years before he eventually joined Chelsea, where he has scored 23 goals in all competitions this, including 11 in his last six games.
Palmer, who scored four times in Monday's 6-0 rout of Everton, was a constant threat for Chelsea, but ultimately it was his team's lack of killer instinct that proved decisive.
Guardiola relief
Palmer's pin-point pass sent Jackson racing into the City area early on, but his strike lacked the accuracy to beat Stefan Ortega in a miss that foreshadowed Chelsea's fate.
Jackson wasted a golden opportunity to give Chelsea the goal their dominance deserved.
Enzo Fernandez's pass split the City defence, but Jackson opted to go around Ortega rather than shoot and the chance was gone as Nathan Ake scurried back to clear.
Playing with more purpose and quality than City, Pochettino's team threatened again as Palmer cleverly shimmied past Rodri for a low drive from 12 yards that was well saved by Ortega.
It was the first time lethargic City had failed to muster a first half shot on target since a game against Everton in February.
Jackson, in the midst of a terrible debut season, was put clean through on goal by Conor Gallagher immediately after the interval.
But the much-maligned striker's shot was palmed away by Ortega, who clawed away a close-range header from Jackson seconds later.
City finally tested Djordje Petrovic through Phil Foden's snap-shot, but the Serbian was equal to his powerful strike.
Chelsea appealed in vain for a penalty when Jack Grealish's arm blocked Palmer's free-kick, while Moises Caicedo was fortunate to escape a second booking for a crunching tackle that forced Grealish to limp off.
Grealish's replacement Jeremy Doku drew an immediate save from Petrovic with a near-post blast.
Doku's presence lifted City and the Belgian played a part as they stole the victory in the 84th minute.
Advancing with intent towards the Chelsea area, Doku slipped a pass to Kevin de Bruyne, whose low cross was pushed out by Petrovic to Silva for a close-range finish that deflected home as Guardiola punched the air in relief.