In a hard-fought fifth-round tie at the Weston Homes Stadium, the Championship side kept City at bay in the first half, but a moment of quality from Mahrez broke the deadlock on the hour mark.
Find how when the draw for the next round is and how you can follow it below.
WHEN IS THE DRAW?
The quarter-final draw is on Thursday March 3, prior to the fifth round tie between Everton and Boreham Wood, with coverage of the programme starting at 19:30 (UK).
HOW CAN I FOLLOW THE DRAW?
Fans based around the world can find out how they can tune in via the FA’s list of global broadcast partners.
WHAT BALL NUMBER ARE CITY?
City are ball number three in the draw.
1 - Chelsea
2 - Crystal Palace
3 - Manchester City
4 - Liverpool
5 - Southampton
6 - Middlesbrough
7 - Nottingham Forest or Huddersfield Town
8 - Everton or Boreham Wood
WHEN WILL THE QUARTER-FINALS BE PLAYED?
The quarter-final ties will be played between Friday 18 March and Monday 21 March.