De Gea played down his role, saying it was simply a "good game for me" before focusing on the "confidence" United can take into next week's Manchester derby at Old Trafford.
Manchester United coach Jose Mourinho talks with Manchester United's Paul Pogba, right, during the English Premier League soccer match between Arsenal and Manchester United at the Emirates stadium in London, Saturday, Dec. 2, 2017.
United's fourth successive league win puts pressure on City to maintain their blistering form against West Ham on Sunday.
They'll be hoping to close the eight point gap on rivals Manchester City this evening when they face Arsenal at the Emirates.
Antonio Valencia intercepted a poor pass from defender Laurent Koscielny that was meant for wing back Sead Kolasinac.
Nacho Monreal failed to spot that Valencia had carried on his run and Pogba slipped the ball to the Ecuador defender, who drilled a clinical finish past Petr Cech.
PA Arsenal are in red-hot form at home
Laurent Koscielny's careless cross-field pass inadvertently set up Valencia's opener before Shkodran Mustafi's carelessness in possession led to Lingard scoring, the England global not even having to break stride to convert Anthony Martial's exquisite reverse pass in behind.
Martial steered a deft pass into Lingard's path and the United winger kept his cool to shoot low into the far corner for his fifth goal of the season. Midfielder Aaron Ramsey was onside when he touched the ball back to Lacazette who fired it past de Gea.
"It's a mystery [we did not score more] but he [De Gea] was the man of the match by a mile", said Wenger.
In a thrilling end-to-end contest United looked irresistible on the break but Arsenal enjoyed more than 70 percent of possession in the first half, hitting 15 shots as David De Gea's goal led a charmed life.
In the 73rd minute, the visitors were reduced to 10 men when Paul Pogba was shown a straight red for a studs up challenge on Bellerin.
But with De Gea in defiant mood, United had done enough for a memorable success.