© PA Photos
The hosts saw plenty of the ball in the opening stages, but lacked the incisiveness needed in the final third.
Robin van Persie then forced Hugo Lloris to make a save after he nodded Phil Jones's cross towards goal.
The first real opportunity fell to the hosts, as Aaron Lennon worked his magic wide on the right before drifting inside and unleashing a fizzing left-footed effort.
De Gea got down low to make the save, but then Jermain Defoe bore down on goal from the rebound.
The United stopper got up quickly to deny the England striker, whose goal would not have counted anyway, as the lineman had raised his flag.
The home side responded positively and could have drawn level had it not been for De Gea. Defoe tried to catch the Spaniard out at his near post, but the 22-year-old was alert to the danger and tipped the ball away from danger.
He then used all of his ingenuity to stop Gareth Bale from equalising, using his foot to block the ball after the Welshman's shot had sent him the wrong way.