A limp 2-0 home defeat before the international break left City eight points adrift of unbeaten Premier League leader Liverpool, a gap cut to five at Selhurst Park, at least for 24 hours.
City dominated the first half but it took until the 39th minute for Jesus's diving header to break the deadlock, with Silva finishing Raheem Sterling's exquisite assist just 93 seconds later.
Pep Guardiola's side failed to add to its advantage after the break but it was not for the want of trying in a one-sided encounter.
Silva disappointingly struck an edge-of-the-box effort straight at Wayne Hennessey, who palmed away a bending Bernardo Silva strike as City roared out the blocks.
Having been frustrated for much of the half, a quick-fire double had City in control.
Jesus stooped low to head home Bernardo Silva's fine whipped cross off the right post for his 50th City goal before David Silva drilled a volley through Hennessey's legs from Sterling's wonderful chipped pass.
Kevin De Bruyne was lucky to escape punishment for a high boot on Cheikhou Kouyate, but there was no City let up after the break and Sterling rattled the outside of the left upright with a near-post drive.
Anthony Taylor dismissed a De Bruyne penalty claim after a shove from Wilfried Zaha and Jesus's left-foot stinger was well saved at full stretch by Hennessey, who also did well to tip over Bernardo Silva's dipper.
Ederson stunningly tipped substitute Christian Benteke's header on to the bar in a rare Palace threat, but Jesus and Sterling missed further chances and De Bruyne also rattled the post in a routine City win.
City welcomes Atalanta to Etihad Stadium for a UEFA Champions League clash on Wendesday (AEDT), while Palace makes the short hop across London to visit Arsenal a week on Monday (AEDT).