Spanish midfielder Silva scored a stunning opener in the 14th minute at the KC Stadium and set up a late Edin Dzeko strike as City survived the early dismissal of captain Vincent Kompany.
Victory for Manuel Pellegrini’s men represents the first step in their task of reeling in league leaders Chelsea.
Chelsea manager Jose Mourinho has been at pains to stress that the advantage lies with City, but, with points on the board, few genuinely believe he would readily swap places.
Mourinho’s mind games aside, the pressure on City is palpable as they look to play catch-up after seeing two other chances of silverware vanish in less than a week.
Pellegrini’s side lifted the League Cup at the start of the month, but were knocked out of the FA Cup by Wigan Athletic last weekend before going out of the Champions League at Barcelona’s hands in mid-week.
Pellegrini made four changes to the team beaten 2-1 in Wednesday’s game at the Camp Nou, including bringing in Dzeko in place of injured striker Sergio Aguero.
Beyond taking the lead, Steve Bruce’s Hull could hardly have wished for a more encouraging start as City were a man down after 10 minutes.
Nikica Jelavic had already caused problems for the City defence with his physical presence and he capitalised on a moment’s hesitation by Kompany.
The City captain’s response was to haul the Croatian to the floor and, as the last defender, a red card was inevitable, ruling the Belgian out of next weekend’s home match against Fulham.
Pellegrini adjusted his team by dropping Javi Garcia into defence alongside Martin Demichelis, and the visitors’ response was almost instant.
– Hart enraged by Boyd –
After Hull failed to close City down quickly, Yaya Toure’s neat pass found Silva in a central position, 25 yards out, and the Spaniard’s left-foot strike left goalkeeper Allan McGregor helpless.
City were close to doubling their advantage when a half-clearance found its way to Pablo Zabaleta and the Argentine’s volley crashed off the underside of the bar and onto the goal-line before being cleared.
The numerical advantage meant that Hull saw more of the ball than they might have expected, while Bruce reacted by bringing on forward Sone Aluko for defender Maynor Figueroa at half-time.
It sent out a positive message and Hull took the game to their visitors.
Shane Long’s smart turn and shot from 18 yards after good work from James Chester was beaten away by Hart, before the England goalkeeper denied Jelavic, who mishit his shot from Aluko’s inswinging free-kick.
Hull were increasing the pressure and the hosts were convinced that they deserved to be awarded a penalty after George Boyd went down in the area following a challenge from Hart.
Hart clearly believed that Boyd had dived, and was booked for angrily confronting the Hull substitute.
With 18 minutes remaining, City mounted their first attack of the second half and they should have killed off the game.
Silva’s deflected shot found its way to Fernandinho 10 yards out, but the Brazilian somehow managed to shoot wide.
Dzeko was then guilty of squandering a similarly inviting opportunity when, after being put through by Gael Clichy, he could only fire straight at McGregor as the Hull goalkeeper rushed off his line.
But the Bosnia and Hercegovina striker atoned in the 90th minute, latching onto a fine through ball by Silva and firing low past McGregor to seal the victory.