Pearson tapped in from all of a yard for his third goal of the season before half-time, then Collins did likewise after the break for his eighth as he scored at the club he supported as a boy for the second season in a row.
Last time it was a last-minute equaliser, but this one was much more important as it eventually proved the winner, with Coventry pulling a goal back four minutes into injury-time as Jonson Clarke-Harris converted a penalty to ruin what would have been a fourth clean sheet in a row.
It was the only blot on the perfect away performance, and only the fourth goal the Town have conceded in 11 unbeaten league and FA Cup games since the 3-2 defeat at Barnsley in mid-October - a run which includes ten wins.
Overall it is just that one reversal in 17, and remarkably Jones named an unchanged team for the seventh successive game in those two competitions as they cemented their place in the automatic promotion spots, narrowing the gap on Portsmouth to four points with the leaders drawing 1-1 at Barnsley.
The Town boss also picked the same seven players on the bench as for last Saturday's victory over Fleetwood, with Danny Hylton and Luke Berry once again among the game changers.
That meant James Shea was in goal behind a back four of Jack Stacey, Pearson, Sonny Bradley and James Justin.
Captain Glen Rea anchored the midfield, with Pelly-Ruddock Mpanzu, Andrew Shinnie and Elliot Lee, just behind Collins and Harry Cornick.
In-form forward Cornick had the game's first opportunity in the 16th minute when Lee set him clear in the inside-right channel, but after outpacing centre-half Tom Davies, he dragged his shot across Lee Burge's goal and wide of the far post.
Stacey was soon trying to get in on the right, latching onto a pass from Mpanzu, then Bradley headed over the resulting corner as the Hatters looked to make their early domination of the ball tell.
In the 18th minute the hosts had their first chance when Jordy Hiwula got on the end of Luke Thomas' right-wing cross, but Shea somehow managed to prevent his effort from going in, despite Sky Blue appeals that it had gone over the line.
The Hatters were soon on the front foot again, but a scrappy period of play followed with both sides conceding possession, often playing the ball straight out of play under little pressure, as a difficult playing surface and the weather conditions took their toll.
After Shinnie was fouled to the left angle of the City penalty area in the 37th minute, home defender Jack Grimmer did well to head Lee's wickedly inswinging free-kick over his own bar, but the relief was shortlived.
Justin trotted over to the right to deliver the corner that Bradley rose highest to meet at the far post, sending his header back across the six-yard box for his centre-half partner Pearson to stab over the line from a yard out.
Cornick was next to test Burge, racing onto a Collins flick from Shea's long clearance down the left, then cutting in to send a low shot on target from 18 yards, but the home keeper had his body right behind it.
Town started the second half well, skipper Rea firing just over in the 47th minute, but then had to rely on Shea to make another terrific point-blank save from Clarke-Harris' far post header a couple of minutes later.
The advantage was doubled in the 57th minute when Lee tricked his way to the right byline and fizzed a low ball across the six-yard box for Collins to net against the club he supports, at the same end of the Ricoh, for the second season in a row.
Coventry looked to get back into it and just after the hour Thomas beat Stacey and Shinnie out on the left and crossed low for Clarke-Harris, who couldn't sort his feet out quickly enough and the ball trickled wide.
At the other end, Lee was soon beating his man on the left byline, not once but twice, only for his low cross-shot to be turned behind by Burge's outstretched leg - and the Town were denied a third from the resulting corner only by Clarke-Harris heading Rea's blistering half-volley off the line as it headed towards the top corner.
Jones brought Hylton off the bench for Cornick with just over a quarter-of-an-hour to go, but it was Coventry who had the next shot - although Liam Kelly's effort from 25 yards only troubled the empty seats behind the goal and brought ironic chants of 'We've had a shot' from the home fans at the other end!
Hylton teed up Lee for a low shot that skipped up off the greasy surface with five minutes left, but Burge dealt with it well, then Shea made another good save to keep out substitute Dom Hyam's header.
He was exposed deep into injury-time though when Thomas capitalised on hesitation in the Town backline, and Shea raced off his line and brought him down.
Clarke-Harris converted the spot-kick, but the Town had already done enough to head off on their Christmas party in the best possible mood as a sequence of five games in 18 days over the festive period got off to a flyer!
TOWN: Shea, Stacey, Pearson, Bradley, Justin, Rea (c), Mpanzu, Shinnie (Potts 89), Lee, Collins, Cornick (Hylton 73). Subs: Potts, Berry, Hylton, Grant, LuaLua, Sheehan, Stech (GK)
Goals: Pearson 38, Collins 57
Yellows: Mpanzu, Shinnie
COVENTRY: Burge, Grimmer, Willis (Hyam 65), Davies, Kelly (c), Hiwula (Chaplin 65), Brown, Clarke-Harris, Bayliss (Allassani 78), Thomas, Shipley. Subs: Addai (GK), Mason, Doyle, Allassani, Ogogo.
Goal: Clarke-Harris (pen) 90+5
Yellow: Hyam
REFEREE: Charles Breakspear
ATT: 12,559 (2,598 Hatters)
