The outstanding Silva accepted a neat pass from substitute Nasri before sliding the ball back to his team-mate to net from close range. There was a hint of offside, but the 2-0 scoreline hardly flattered the home side.
Chelsea were disappointing as they failed to create any real chances against a team who remain active in all four competitions.
City progress to the last eight with Chelsea forced to concentrate on the Premier League and the Champions League. They can few complaints.
15' - JOVETIC CHANCE: Cech spills a thumping shot by Toure, but Jovetic clips the top of the bar from the rebound. So close to an opening goal from City, who have certainly started brighter.
16' - JOVETIC GOAL: Jovetic slides the ball beyond Cech from the Dzeko pass. Shot goes in off the post. Lovely play from Silva too. César Azpilicueta could not get across to make the block. No chance for Cech. A 1-0 lead for City.
25' - CECH STOP: Another slick move from City ends up with Dzeko driving the shot at goal that sees Cech dive to his right to make a decent save. Some lovely stuff going forward from the home team.
44' - DZEKO ALMOST IN FOR SECOND: Milner slams a lovely ball across the face of the Chelsea goal, but Dzeko just fails to connect. Inches away from the second.`
50' - JOVETIC SQUANDERS OPPORTUNITY: Jovetic ends up lifting the ball miles over the bar from inside the Chelsea box. That was a chance for City but not taken.
67' - NASRI SCORES FOR CITY: Silva looked to be offside, but no flag goes up as he takes the pass from Nasri before setting up Nasri for the second goal. A 2-0 lead for City.
75' - LESCOTT GOAL RULED OFFSIDE: Lescott stabs the ball into the net after Cech spills the Garcia header, but he is just offside. We remain at 2-0 in the home side's favour.
Chelsea only had two shots against Manchester City today; both were from outside the area and both were off target.
Chelsea have lost just two of their last 33 FA Cup games, winning 25 and drawing six.
Costel Pantilimon did not make one save City in the 2-0 FA Cup victory.
TALKING POINT: Will Joleon Lescott start against Barcelona on Tuesday? Has done himself no harm. Had a goal ruled offside, and looked very comfortable alongside Kompany in his first start in three weeks. Is he a safer bet than Matija Nastasić or Martin Demichelis? Manuel Pellegrini must review his options before the first leg against the Spanish champions.
MAN OF THE MATCH
Vincent Kompany (Manchester City): So many players in the City side were up for this nomination - including Yaya Toure and David Silva - but Kompany gets the nod. Alongside Joleon Lescott, Kompany coasted through the evening.
Manchester City: Pantilimon 6, Zabaleta 7, Kompany 8, Lescott 8, Clichy 7, Garcia 7, Toure 8, Milner 7, Silva 8, Jovetic 7, Dzeko 7...subs: Navas 6, Negredo 6, Nasri 7
Chelsea: Cech 6; Ivanovic 6, Cahill 6, David Luiz 6, Azpilicueta 6; Mikel 5, Matic 5; Ramires 5, Willian 5, Hazard 5; Eto'o 4..subs: Salah 5, Oscar 5, Torres 6
THE MATCH IN A TWEET