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Third-tier Luton put up a resolute defensive performance at Stamford Bridge, but Welbeck finally broke its resistance early in the second half, and an unfortunate Hakeem Odoffin own goal made sure of Chelsea's victory.

Having won its first two competitive games under Alonso, Chelsea will now face Leeds United in an all-Premier League tie in round three next month. 

Chelsea set up camp on the edge of Luton's area for practically the entire first half, but none of their 17 shots before the interval beat Josh Keeley in the Hatters' net.

Morgan Rogers went closest to opening the scoring in the first half as he rattled the crossbar in stoppage time, while Estevao also dragged an effort wide when clean through on goal and Reece James drew a fine save out of Keeley after a free-kick routine.

Luton could only hold out for five minutes of the second half, though, as Welbeck met Malo Gusto's right-wing cross with a bullet header to give Keeley no chance.

Welbeck passed up a decent chance for his brace soon afterwards, after a deft through-ball from Palmer, who later clipped the top of the crossbar with a dipping effort from 20 yards out.

The Hatter's slim hopes of a fightback were dashed in the 79th minute, as Odoffin sliced Estevao's cross, which appeared to be drifting wide, into the roof of his own net, and Chelsea went close to adding further gloss on two occasions in stoppage time, with Keeley denying Palmer and substitute Jamie Gittens hitting the base of the post.