The Spain playmaker secured City's fourth straight league win by scoring in the 2nd and 69th minutes for his first goals in two months, increasing the pressure on United ahead of its testing visit to Tottenham on Sunday.
"All we can do is win our games," City assistant manager David Platt said. "We have to make sure we keep getting victories so if United do slip up, we are in a position to take advantage of that."
Liverpool thrashed Norwich 5-0 to revive hopes of qualifying for European competitions next season, with Luis Suarez and Daniel Sturridge striking up a good combination up front and both getting on the scoresheet at Anfield.
France striker Loic Remy scored on his debut for Queens Park Rangers but a 1-1 draw at West Ham kept the club bottom of the standings, five points adrift of safety after Reading's 2-1 come-from-behind win over struggling Newcastle and Aston Villa's 2-2 draw at West Bromwich Albion.
Wigan replaced Villa in the bottom three after losing 3-2 at home to Sunderland, while Swansea beat Stoke 3-1 in the other match.
With United winning the last four games in its bid for a 20th league title, City knows it cannot afford any more mistakes in the run-in and the defending champions did their job against Fulham, without ever finding their best form.
Silva provided the cutting edge, following up Mark Schwarzer's save from a long-range shot from Edin Dzeko to plant a rebound into the bottom corner after just 95 seconds to make it 1-0. He then ensured there was no way back for Fulham by running onto Carlos Tevez's flick and chipping home a deft finish.
"David Silva was the best player on the pitch and he was fantastic, a quality player," said Fulham manager Martin Jol, who acknowledged his team is in a "relegation battle."
"To concede in the second minute is a horrific scenario."
With Chelsea and Arsenal not meeting until Sunday and fifth-place Everton in action on Monday at Southampton, Liverpool had a chance to pull closer to the teams above them in the race for the remaining European spots behind the Manchester clubs.
It had no trouble, with Norwich meekly surrendering and taking the number of goals the team has conceded against Liverpool in their last three matches to 13.
Luis Suarez, back in the headlines for the wrong reasons this week after admitting diving in an early-season league match, showed his good side by helping set up Jordan Henderson's spectacular opener and then slotting in the second for his 16th of the campaign.
Liverpool manager Brendan Rodgers reserved special praise, however, for Sturridge after the striker continued his goal-a-game start to his Liverpool career by scoring in the second half along with Steven Gerrard and an own goal by Ryan Bennett.
"He is terrific outside the box but he is a real killer in it," Rodgers said. "It's three goals in three games for him and I think there will be many to come. We have played well for most of the season but Daniel coming in adds that extra threat."
Liverpool is three points behind Everton having played a game more and a point ahead of Swansea, which warmed up for the second leg of its League Cup semifinal against Chelsea by downing Stoke thanks to two goals by Jonathan De Guzman.
Michael Owen scored Stoke's consolation — his maiden goal for the club, 150th in the Premier League and first in any competition in nearly 15 months.
Joe Cole's first goal in his second spell for West Ham denied Remy a dream debut for QPR following his club-record move from Marseille on Wednesday, for a reported 8 million pounds ($12.7 million).
"We are still (bottom) but we are in much better shape that we were six or seven weeks ago," QPR manager Harry Redknapp said. "There will be teams looking over their shoulder."
Adam Le Fondre came off the bench to boost Reading's survival hopes, scoring both the team's goals to leave Newcastle just two points off the bottom three.
"That was a tough defeat for us," said Newcastle manager Alan Pardew, whose team finished sixth last season to qualify for the Europa League.
Reading is third from bottom — a point behind Villa, which surrendered a two-goal lead at The Hawthorns when Peter Odemwingie equalized for West Brom in the 83rd minute.Suggest a correction