Match ends, Chelsea 3, Luton Town 1.
A Tammy Abraham hat-trick earned Chelsea victory over Luton Town in the FA Cup fourth round to relieve some pressure on manager Frank Lampard.
Abraham slotted in from Timo Werner's cut-back before nodding in a second from Reece James' chip.
Jordan Clark scored for the visitors - after an error by keeper Kepa Arrizabalaga- on 30 minutes to keep them in the game.
But Abraham poked home to seal victory before Timo Werner missed a penalty.
Chelsea will face Championship side Barnsley in the fifth round.
- Chelsea v Luton as it happened, plus updates from the rest of Sunday's FA Cup fourth-round ties
- Watch all the goals from the FA Cup fourth round
Chelsea - who won the competition in 2018 and were beaten finalists last season - were in complete control at 2-0 and Christian Pulisic and Abraham both went close to increasing their lead.
But Luton, who edged past Reading in the last round, settled into the game after James Bree crossed in for Clark to squeeze his shot under Kepa, who should have done better.
The Blues were sloppy at times in the second half and Luton had chances, Kepa saving from Harry Cornick and Tom Lockyer to redeem himself after the earlier error.
Callum Hudson-Odoi replaced Pulisic on 70 minutes and made an immediate impact, having a shot blocked with with his first touch before setting up Abraham with a low cross for Chelsea's third goal.
Werner, who scored his first goal in 13 games against Morecambe in the third round, had the chance to make it 4-1 five minutes from time after being tripped in the box by Clark, but saw his spot-kick saved by Luton keeper Simon Sluga.
It was a welcome victory for Lampard, who has come in for criticism over Chelsea's Premier League position - they sit ninth in the table after five defeats in their past eight games.
'Hard to leave Gilmour out' - what they said
Chelsea boss Lampard: "Playing like he did today it will be very difficult to leave Billy Gilmour out because he was outstanding.
"His comfort on the ball, the way he moves it, his discipline, personality on the team. He was brilliant.
"In the short term, he won't be going on loan. Billy is a Chelsea player and his levels today showed that it's right he's a Chelsea player in the middle of the park."
Luton manager Nathan Jones: "It was a great test for us and I'm very proud of the game we gave Chelsea.
"We gave ourselves a mountain to climb in the first 20 minutes, but I will accept responsibility for that because I wanted us to be attacking in our shape and do more than just defend.
"Once we changed that shape I thought we were excellent."
Best of the stats
- Chelsea have reached the fifth round of the FA Cup in 21 of the past 23 seasons, only failing in 2010-11 and 2014-15.
- Luton have been knocked out in their past six domestic cup ties against Premier League opposition.
- Chelsea have won 18 of their past 21 FA Cup games at Stamford Bridge, including all four home matches in the competition since the start of last season.
- Abraham became the first Chelsea player to score an FA Cup hat-trick since Oscar against MK Dons in January 2016, and the Englishman to do so since Lampard got three goals against Macclesfield in January 2007.
- 19MountSubstituted forKovacicat 84'minutes
- 22ZiyechSubstituted forHavertzat 77'minutes
- 10PulisicSubstituted forHudson-Odoiat 70'minutes
- 9AbrahamSubstituted forGiroudat 77'minutes
- 26BreeSubstituted forLuaLuaat 61'minutes
- 16ReaSubstituted forPottsat 45'minutes
- 24NaismithSubstituted forMoncurat 75'minutes
- 4TunnicliffeSubstituted forBerryat 61'minutes
- 18ClarkBooked at 85mins
- 7CornickSubstituted forCollinsat 60'minutes
- David Coote
- Shots on Target
Second Half ends, Chelsea 3, Luton Town 1.
Attempt saved. Olivier Giroud (Chelsea) right footed shot from the centre of the box is saved in the centre of the goal.
Attempt blocked. Olivier Giroud (Chelsea) left footed shot from outside the box is blocked.
Billy Gilmour (Chelsea) wins a free kick in the defensive half.
Foul by James Collins (Luton Town).
Kai Havertz (Chelsea) wins a free kick in the defensive half.
Foul by Sonny Bradley (Luton Town).
Attempt missed. Callum Hudson-Odoi (Chelsea) right footed shot from the left side of the box misses to the right. Assisted by Emerson.
Offside, Chelsea. Callum Hudson-Odoi tries a through ball, but Timo Werner is caught offside.
Penalty saved! Timo Werner (Chelsea) fails to capitalise on this great opportunity, right footed shot saved in the centre of the goal.
Jordan Clark (Luton Town) is shown the yellow card for a bad foul.
Penalty Chelsea. Timo Werner draws a foul in the penalty area.
Penalty conceded by Jordan Clark (Luton Town) after a foul in the penalty area.
Substitution, Chelsea. Mateo Kovacic replaces Mason Mount.
Corner, Luton Town. Conceded by Emerson.
Emerson (Chelsea) wins a free kick in the defensive half.
Foul by Kazenga LuaLua (Luton Town).
Hand ball by Olivier Giroud (Chelsea).
Offside, Luton Town. Jordan Clark tries a through ball, but Luke Berry is caught offside.
- All the goals, highlights and drama from Saturday's fourth-round ties are streaming now on BBC iPlayer