An own goal from Leander Dendoncker put City ahead in the first half, but City were almost made to pay for failing to build on their domination of possession as Conor Coady levelled with a header just past the hour-mark.
With Pep Guardiola facing the prospect of seeing City’s 20-game winning run go up in smoke, the table-toppers stepped things up late on as Jesus put the hosts back in front 10 minutes from time.
Mahrez made the game safe with a well-taken finish in the 90th minute, while Jesus added his second of the night with the last touch of the game as the goal – initially ruled out for offside – was awarded following a VAR review.
The result sends City 15 points clear of Manchester United before the Red Devils play on Wednesday night, and cements City’s status as champions-elect.
They are now only two short of equalling Bayern Munich’s record 23 successive wins for a top-flight from any of Europe’s recognised ‘top five’ leagues and six behind Welsh side TNS’ world record.