Middlesbrough produced another FA Cup shock to extend Tottenham's long wait for silverware with a 1-0 win after extra time at the Riverside on Tuesday, while Manchester City eased into the last eight with a 2-0 victory at Peterborough.
Boro knocked out Manchester United at Old Trafford in the fourth round and the Championship side were worthy winners to condemn Spurs to another trophyless season.
Not since a League Cup win in 2008 have Tottenham lifted a trophy and another hugely disappointing defeat poses further questions over the future of manager Antonio Conte.
The Italian only took charge in November, but has already hinted he could walk away after a run of four defeats in the past six Premier League games.
Teenager Josh Coburn came off the bench to score the only goal with a thumping finish across Hugo Lloris in the 107th minute.
Chris Wilder's men might not have been forced to play the extra 30 minutes had Matt Crooks connected with a free header from a corner.
Harry Kane did have the ball in the net for Tottenham only to be flagged offside.
But the England captain may also be again considering his future as he waits to win the first major honour of his career.
Middlesbrough were by far the brighter side in extra time and got their reward when Coburn rifled across Lloris from Crooks' through ball.
Once the action got underway, Guardiola's men took time to make the breakthrough against a side sitting bottom of the Championship.
Mahrez took his tally for the season to an impressive 19 goals in just 32 appearances as the Algerian cleverly guided the ball into the far corner from a narrow angle on the hour mark.
Grealish has had a far less productive season since his £100 million move from Aston Villa.
But he marked his return from injury with a sublime touch to control Phil Foden's long through ball before slotting past Steven Benda for his fourth City goal.
"While we were on the coach on the way to the game, I was sat next to Phil and we were scrolling through videos of (Lionel) Messi," said Grealish.
"After scoring he came up to me and said it was just like we were watching."
Crystal Palace also booked their place in the quarter-finals with a 2-1 win over Stoke.
Cheikhou Kouyate and Jairo Riedewald struck for the Eagles either side of Josh Tymon's equaliser.