Silva, out for a fortnight after suffering a blow to his knee during the FA Cup semi-final defeat by Arsenal, struck inside the first two minutes.
Second-half goals from Vincent Kompany, Kevin De Bruyne, Raheem Sterling and Nicolas Otamendi completed the scoring as City leapfrogged Liverpool into third in the Premier League, on goal difference, and also moved four points clear of fifth-placed Manchester United.
Only the top four at the end of the season qualify for the Champions League, European club football's leading competition, with City now having three Premier League games left to play this term.
But both Liverpool (at home to Southampton) and United (away to Arsenal) are in action Sunday.
For Palace, not yet safe from the threat of relegation, Saturday's reverse was their third straight defeat.
City manager Pep Guardiola has spoken repeatedly over the last two months about his side's failure to make possession and chances count, citing that as a reason for their relatively disappointing season.
He would have been pleased that his side scored from their first attack, but not that they then passed up a series of first-half opportunities to add to that lead.
The goal, City’s fastest in any game this season, was well-worked, with Spanish playmaker Silva starting and finishing the move.
Silva, making his 200th Premier League start, angled a chip towards Sterling and then, when the cross was half-cleared by Martin Kelly, timed his run perfectly to side-foot a volley into the corner of the net.
For much of the opening half-an-hour, it seemed inevitable that more goals would follow, as Palace offered little midfield resistance.
But a combination of poor final passes and sound goalkeeping from Palace's Wayne Hennessey prevented City from increasing their tally for a while.
City might even have lost their lead 10 minutes before half-time, when Palace's Andros Townsend got down the right to cross, Christian Benteke climbed above stand-in right-back Fernandinho to head down, and Willy Caballero twisted to his left to make a fine one-handed save.
Haf-time arrived with City in danger of being drawn into a scrap, with De Bruyne twice kicked by Jeffrey Schlupp, and Silva taking matters into his own hands by retaliating with a wild hack at Wilfried Zaha.
However, Guardiola's side recovered a degree of composure at half-time, and extended their lead three minutes after the restart.
After De Bruyne's corner had been cleared, Silva worked the ball back to the Belgium international, who rolled a pass inside for compatriot Vincent Kompany to sweep in with a vicious first-time shot.
That appeared to settle City down, and De Bruyne almost made it 3-0 with a dipping 25-yard free-kick that brushed the top of the crossbar.
More chances followed and third goal City had been threatening arrived shortly before the hour mark when the influential De Bruyne steered a shot under Hennessey and just inside the post after Sterling had held off Schlupp to reach Silva’s header and set up the chance.
By now, City were cruising, and the fourth goal had the feel of a training ground exercise about it.
Yaya Toure had all the time he wanted to play a diagonal ball towards substitute Pablo Zabaleta, who guided a header back for Sterling to finish from 20 yards.
There was more to come. In stoppage time, Palace switched off at a De Bruyne free-kick, allowing Otamendi to dive and head in to make it 5-0.