Nizaar Kinsella
BBC Sport Chelsea reporter

New boss Xabi Alonso wears a smile after a win in his first home game as Chelsea manager, although he is in discussion with referee Elliot Bell following a bizarre substitution incident after the final whistle.

Fourth official Sunny Singh Gill would not allow Joao Pedro onto the pitch, forcing Chelsea to play with 10 men for a brief period.

It had little impact on the outcome but was a curious moment.

Luton's supporters, meanwhile, have been superb and remained behind to applaud their team, who battled impressively and kept the scoreline to two goals despite the gulf in resources between the clubs.

It is job done for Chelsea, who next face Leeds United in the Carabao Cup next month.

The Wimbledon fans are having a great time at Craven Cottage tonight, even though they trail by two goals.

They're all bouncing up and down, having a party in that away end.

Luc De Fougerolles is riddled with a nasty bout of cramp.

We've all been there and it's not nice.

Kenny Tete makes the first contact from Harrison Reed's ball in but he's always reachig and he can't get the direction needed.

Kevin goes on the inside of the Wimbledon defence, plays a wall pass off Ryan Sessegnon and looks to slip it past Nathan Bishop but the keeper makes the save.

Job done for Xabi Alonso's side.

Chelsea progress to round three.

And now Calvin Bassey comes on to replace Joachim Andersen.

Macauley Zepa looks a tidy player.

He comes in off the right and tries to find the angle for a curling effort but it's charged down.

Chris Sutton
Former Chelsea striker on BBC Radio 5 Live at Stamford Bridge

Chelsea thoroughly deserve the victory, they have been the superior team.

Luton have been dogged and hung in there.

They certainly haven't disgraced themselves and they should take a great deal of pride with the way they have performed this evening.

And Joao Pedro very nearly gets his goal to make it 3-0 but Josh Keeley pounces on it.

Keeley keeps out Cole Palmer with his foot first and then is quick to react to Joao Pedro's rebound.

We're into four minutes of added time.

Harrison Reed's corner isn't dealt with by Nathan Bishop but Wimbledon manage to hack it clear.

The keeper hasn't looked convincing at all from corners.

Myles Hippolyte has a go from range. He hits it well enough but it's always rising.

Now time for the age-old chant of 'Is there a fire drill?' as some Chelsea fans make their way to the Tube.

Oles and applause from the Luton fans as they enjoy watching their side enjoy a nice spell of possession.

They play some decent stuff, do Jack Wilshere's side.

A fifth and final Chelsea change as Jamie Gittens replaces Estevao.

For Luton, Devante Cole and Nahki Wells replace Callum Marshall and Kasey Palmer.

Macauley Zepa stands one up to the far post and Rodrigo Muniz shins the most audacious of overhead kicks over the top.

Would've been quite the goal.

Image source, Getty Images

Chris Sutton
Former Chelsea striker on BBC Radio 5 Live at Stamford Bridge

Just when Jack Wilshere had really gambled going with two up top, Hakeem Odoffin put it into the roof of the net.

It feels like it is the end for Luton, they're not going to come back from this unless there is some sort of miracle.

They have defended heroically this evening but it looks like game, set and match for Chelsea.

Unless something miraculous happens, Chelsea will host Leeds in the third round.

Kenny Tete takes things into his own hands, quite literally, as he handballs when trying to referee the game.

Rightly carded.