On a chilly December evening, James Shea produced a brilliant performance between the sticks, first denying Jordy Hiwula from close range before Pearson opened the scoring from a corner.
Shortly after Shea stopped Jonson Clarke-Harris from point-blank range, Collins made it two just before the hour after good work from Elliot Lee on the wing.
His low cross was turned in at the front post in front of the travelling Hatters at the Ricoh Arena.
Shea added yet another impressive save to his reel to keep out substitute Dom Hyam’s header before he brought down Luke Thomas in added time, unable to hang onto a fourth consecutive clean sheet as Clarke-Harris dispatched confidently from the spot.
Coventry: Burge; Grimmer, Willis (Hyam 65), Davies, Brown; Bayliss (Allassani 78), Kelly, Shipley; Thomas, Hiwula (Chaplin 65); Clarke-Harris.
Clarke-Harris (90+5 pen)
Luton: Shea; Stacey, Bradley, Pearson, Justin; Rea, Mpanzu, Shinnie (Potts 89), Lee; Cornick (Hylton 73), Collins.
Pearson (38), Collins (57)
Highlights from that match can be found on our YouTube channel below…