First-half goals from Wayne Rooney and Juan Mata and a third after the break from Robin van Persie saw Louis van Gaal’s side consolidate third in the table and close to within five points of second-placed Manchester City.
However, their defensive frailties were all too apparent throughout the game and they were hugely indebted to De Gea, who produced no fewer than six excellent saves in a superb performance.
Liverpool had little trouble creating chances against United’s porous back three, but defensive errors of their own and a mistake from the officials for Mata’s goal ensured they remain ninth in the table, seven points adrift of the top four.
Brendan Rodgers’s side started with pace and intensity and should have taken the lead when Adam Lallana slipped in Raheem Sterling after 12 minutes, but the England winger saw his low left-footed shot saved by the alert De Gea.
United immediately went down the other end and scored through Rooney, who side-footed home from the edge of the penalty area after Antonio Valencia eased past Joe Allen on the right wing and cut the ball back beautifully.
The goal settled the hosts down and they enjoyed more possession, yet it was Liverpool who continued to create the better opportunities. After Steven Gerrard had seen a right-foot strike from distance deflected into the arms of De Gea, the Spanish goalkeeper produced another point-blank save after 23 minutes to once again deny Sterling, who had skipped past a static Phil Jones in the left channel.
The visitors were then made to pay for their profligacy when Mata doubled the lead by nodding home unmarked at the back post on 40 minutes, although they were not helped by the officials failing to spot that Van Persie had flicked Ashley Young’s left-wing cross on to the Spaniard, rendering him a couple of yards offside.
Liverpool started quickly once again in the second half and should have been level within six minutes. However, Jordan Henderson sent a free header in the box inexplicably over, before De Gea produced yet another superb piece of goalkeeping to block a low shot from Sterling, who had pounced on a tame backpass from Ashley Young and was through one-on-one.
But De Gea’s best save was kept for half-time substitute Mario Balotelli, who looked stunned when he saw the United goalkeeper tip his goalbound shot on to the crossbar after 67 minutes.
Liverpool appeared buoyed by the chances they were being afforded, but all belief then drained out of them when Van Persie added United’s third after 71 minutes.
Dejan Lovren made a horrible mess of clearing Rooney’s cross and presented the ball straight to Mata, who could have shot but instead spread the ball right for the unmarked Dutchman to side-foot home.
De Gea’s virtuoso display was not yet over, though, because he denied Balotelli twice more, first clawing a low shot out of the bottom corner eight minutes from time and then blocking the disbelieving striker’s effort when through one on one five minutes later.
Manchester United: De Gea (9), Valencia (7), Jones (6), Evans (6), Young (6), Carrick (7), Fellaini (6), Mata (7), Rooney (7), Van Persie (8), Wilson (6).
Used subs: Herrera (6), McNair (6), Falcao (6).
Liverpool: Jones (5), Johnson (6), Skrtel (6), Lovren (4), Moreno (6), Henderson (6), Allen (6), Gerrard (6), Coutinho (6), Lallana (6), Sterling (6).
Used subs: Toure (6), Balotelli (6), Markovic (6).
Man of the match: David De Gea.
Highlights of Manchester United v Liverpool are available to Sky Go subscribers.