Silva volleyed home with just four minutes remaining to give the Primera Liga side a psychological edge ahead of the Champions League last-16 second leg at the Mestalla in two weeks' time.It was a better result than performance for Los Che, who were second best for much of the contest against an Inter side which failed to capitalise on their superiority.
Esteban Cambiasso headed the hosts in front after 29 minutes only for David Villa to fire home a spectacular equaliser with a 30-yard free-kick 19 minutes into the second half.
Brazilian full-back Maicon looked to have won it for Inter when his marauding run and composed finish put the Nerazzurri back in front, but Valencia displayed the stubbornness which has seen them surge up the Primera Liga table recently by finding a second equaliser.
Inter dominated the opening half and the only surprise was the fact they did not score more than the one goal.
The onslaught started immediately with Dejan Stankovic heading wide inside three minutes.
And it continued as the minutes passed.
Hernan Crespo shot wide, Zlatan Ibrahimovic headed against the post and the Swedish international came close again shortly afterwards with an effort which fizzed wide of Santiago Canizares' upright.
Valencia's top scorer Villa was a constant threat on the break and the Spain striker twice came close to snatching a priceless away goal.
His first effort was comfortably gathered by Inter keeper Julio Cesar but the second produced a fine parry from the Brazilian.
Despite the flurry of activity at the other end, Inter soon regained control and took the lead approaching the half-hour mark.
Luis Figo whipped in a free-kick from the right which Ibrahimovic somehow directed on target with the sole of his boot and, when Canizares could only parry it into the air, Cambiasso was on hand to nod home from close range.
Inter ought to have made it 2-0 after 42 minutes but Crespo, normally so deadly in front of goal, put his header wastefully wide following a pin-point cross to the far post by Stankovic.
Having been outplayed for the majority of the half, Valencia came within inches of equalising on the stroke of half-time when Villa found himself clean through only to drag his shot wide of the far post.
The second half continued with Inter in charge and it required some fine defending from full-back Miguel to prevent Figo from getting a free shot on target.
Miguel's efforts enabled Valencia to keep a foothold in the game and they strengthened their position after 64 minutes when Villa lashed home a stunning 30-yard free-kick which curled around the wall and into the top right-hand corner.
Figo had the chance to match Villa's effort four minutes later but the Portuguese star could only dink his shot over the bar.
Maicon restored Inter's advantage when he burst forward, played a one-two with Julio Cruz and then slotted past Canizares.
But Inter could not hold on and, after they failed to clear Villa's right-wing corner, Silva was on hand to convert with a crisp shot.
Internazionale 2 - 2 Valencia
