Tammy Abraham gave the hat-trick that eased Chelsea’s nerves and put them into the fifth round of the Cup.
Frank Lampard men wasted several chances to make this victory against a mid-table Championship side far less worrying than it needed to be.
And erratic Kepa Arrizabalaga’s now trademark blunder followed by a world-class save only fuelled the debate around their enigmatic reserve keeper.
Abraham’s first two goals came in the 11th and 17th minutes and Luton looked set to be blown away by a Chelsea team looking to take out its Premier League frustrations on them in the FA Cup.
And finally, Abraham confirmed Chelsea’s place in the last 16 and an away day at Barnsley by turning home a cross from sub, Callum Hudson-Odoi.
But to add a final irksome note for Lampard, out-of-form striker Timo Werner had an 85th-minute penalty saved after being tripped on a run through to goal.