City restored their gap at the top of the table to six points over Liverpool, who have a game in hand, after Jurgen Klopp's team had trimmed the lead down to three with a win over West Ham United on Saturday.
However, the hosts retook the lead soon after when De Bruyne netted his second of the opening 45 minutes following a poor United giveaway that led to a scramble in front of De Gea to give Pep Guardiola's side a 2-1 advantage at the half.
De Bruyne set up a deserved third for Man City from a corner kick, picking out Mahrez at the top of the penalty area for the Algeria international to smash home a brilliant first-time shot to double his team's lead.
Mahrez scored his brace in second-half stoppage time with a goal that was initially flagged as offside, but VAR found that Alex Telles had played the City attacker onside before he latched on to an Ilkay Gundogan pass and shot over the shoulder of De Gea from a tight angle.
United were without Cristiano Ronaldo and Edinson Cavani through injuries as Ralf Rangnick opted to play Paul Pogba and Bruno Fernandes in forward positions to little effect.
Man City return to Champions League action on Wednesday, taking a 5-0 aggregate lead into a round-of-16 second-leg match against Sporting CP, while Rangnick's side, who dropped down to fifth place after the result, won't play again until a Saturday Premier League test against Tottenham Hotspur.
City have 69 points from 28 games with Liverpool on 63 from 27 matches.
Information from Reuters was used in this story.