It was a return to winning ways for City after last weekend’s disappointing 2-2 draw away to Newcastle United.
Mahrez netted City’s fourth goal with three minutes remaining and becomes the 110th player to reach 50 Premier League goals.
Gabriel Jesus got City’s first and second goals in the 24th and 50th minutes respectively, while Rodri made it 3-0 on 68 minutes.
Burnley pulled a goal back through Robbie Brady a minute from time.
The win temporarily move City to second on 32 points, and are now eight points adrift of leaders Liverpool.
In the other PremierLeague game that was played on Tuesday, 10-man Crystal Palace beat Bournemouth 1-0, at Selhurst Park.
Palace were forced to play most part of the game with 10 men after Mamadou Sakho was sent off in the 19th minute.
Despite the numerical disadvantage, it was Palace who got the only goal of the game thanks to Jeffery Schlupp in the 76th minute.
With the win Palace climb to fifth position on the log on 21 points, just five points off fourth spot.
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