The hosts took the lead after two minutes when striker Elijah Adebayo was tripped just inside the area by visiting defender Jake Clarke-Salter.
The forward dusted himself down to power the spot-kick past Simon Moore for his fourth goal of the season and second penalty in as many home games.
A long Harry Cornick throw was flicked on for Luke Berry to arrive and nod narrowly wide of the target, before Town scored a second in the 18th minute.
A short free-kick was played to Jordan Clark and he dinked the ball back into the area where Kal Naismith rose highest to head across for Cornick, who nodded past the exposed Moore.
The game was then stopped as a Coventry fan was carried away from the stands for medical treatment. When the action resumed, the Hatters made it 3-0 on the half-hour mark.
Cornick did superbly to outmuscle two defenders and reach Tom Lockyer's pass before picking out the run of Berry, who tucked home from close range.
Clark was inches away from a fourth, his header dropping just wide as Coventry finally began to make a fist of it. Martyn Waghorn's backheel was blocked by the home defence and then Dominic Hyam hit the side netting.
However, Luton came on strongly again in eight minutes of stoppage time, scoring in the final 60 seconds, as Lockyer sent James Bree down the right and his cross was flicked on by Cornick for Adebayo to bury his second.
After the break, City looked to try and gain some respectability to the scoreline, as Viktor Gyokeres cut in to test Simon Sluga low down, but they were soon picking the ball out of the net again with 58 minutes gone.
A free-kick out from the back went completely wrong as Berry intercepted to find Cornick, who doubled his tally for the evening via a slight deflection.
Bree looked to get his own name on the scoresheet, flashing narrowly wide of the far post on another foray forward, while Adebayo looked to complete his hat-trick from distance, rifling an effort that forced Moore to cling on gratefully.
Berry had calls for another penalty turned down when he felt his 18-yard drive was handballed, before he combined with Naismith to find substitute Carlos Mendes Gomes, who was denied by the legs of the advancing Moore.
Clark tried his luck from 20 yards, Moore easily gathering, before Cameron Jerome almost opened his league account for the Hatters in the closing stages, nodding off target from Naismith's inviting delivery.