The Algeria international struck twice in the first half to surpass 100 goal involvements in the Premier League and put City in total control.
Burnley had brief respite when a third City effort was disallowed, but Benjamin Mendy's clever finish – his first goal in English football – effectively ended the contest before half-time.
Ferran Torres also got his first league goal for City before substitute Phil Foden crossed for Mahrez to complete his treble and cap a supremely comfortable outing at Etihad Stadium.
Mahrez opened the scoring just six minutes in, slotting home from Kevin De Bruyne's pass after a slick City move that started from a loose James Tarkowski pass.
It was 2-0 16 minutes later, Mahrez skipping into space and firing a shot in off the left-hand post after Burnley's defence switched off from a City throw-in.
Goalkeeper Bailey Peacock-Farrell, making his Premier League debut, saw the ball bounce in off the same upright only for the assistant referee's flag to spare Burnley's blushes, with Gabriel Jesus having headed the ball off the offside Torres.
The reprieve did not last long, De Bruyne given time to clip a cross to Mendy, who turned a controlled finish beyond Peacock-Farrell for his first club goal since a Coupe de France match between Monaco and Marseille in March 2017.
It was 4-0 with 66 minutes gone, Torres side-footing home after Jesus' clever lay-off from a Kyle Walker delivery, and Foden needed just 93 seconds on the pitch before his cross was nodded home by the unmarked Mahrez.
Peacock-Farrell turned the ball into his own net but was spared by another offside call, with De Bruyne crashing a shot off the post in injury time as City made it seven wins in a row against the Clarets by an aggregate scoreline of 28-1.
The win moved City to eighth on the table, six points behind Liverpool, which drew with Brighton and Hove Albion and has played a game more. It also ended a run of six consecutive league games in which City has failed to score more than once.
Burnley is 17th, with five points from nine matches, and has now lost four games in a row at City 5-0. In English football league history, only Notts County has beaten a specific opponent by five or more goals in four successive home games, doing so against Port Vale from October 1893 to February 1907.