First half strikes from James Collins - netting his 150th career goal - and Luke Berry proved enough to see off a spirited Rovers, who hauled themselves back into the game on the stroke of half-time through Jonson Clarke-Harris.
The victory meant that the Hatters equalled the 27-match run without defeat that was set in the Conference title-winning season of 2013-14, having already broken the club’s Football League record last month.
With second-placed Barnsley being held 2-2 at home by Coventry, and third and fourth-placed Portsmouth and Sunderland not in action due to tomorrow's Checkatrade Trophy final, it also meant the Hatters opened up a seven-point advantage over the Tykes having played the same number of games, and a 12 and 13-point cushion over Pompey and the Black Cats.
Mick Harford made two changes, Luke Berry returning to the starting XI after coming on as a first-half substitute for Dan Potts during last week’s 4-0 home win over Doncaster, and top scorer Collins coming straight back into the team after his time away with the Republic of Ireland, replacing Danny Hylton, who didn’t travel with the squad due to injury.
Pelly-Ruddock Mpanzu, the club's longest-serving player, made his 200th appearance for the Hatters in the midfield holding role.
The hosts started brightly, but the Town defended stoutly and managed to break forward to win a couple of early corners, the second of which resulted in a half-chance for Matty Pearson after Sonny Bradley won the initial header, but the centre-half’s shot was blocked.
Berry sent a daisy cutter straight into keeper Jack Bonham’s hands soon after, but it was Rovers who had arguably the clearest opening of the opening quarter-of-an-hour, top scorer Jonson Clarke-Harris cutting in from the left and crossing low for strike partner Tom Nichols, whose shot was cleared from inside the six-yard box by James Justin.
The breakthrough came in the 17th minute, and it was Collins who was there to steer in his 21st goal of the season after good work from Elliot Lee found Andrew Shinnie to the right side of the Rovers penalty area.
The Scottish midfielder slipped Jack Stacey in to the byline and the right-back fizzed an inviting ball across the six-yard box for Collins to bag his first goal in four matches.
The Town's next opportunity came on 28 minutes after good work down the left by Justin, Berry and Lee, but Kazenga LuaLua's attempted curler towards the top corner was too high.
Three minutes later it was Berry's turn, after another incisive counter-attack down the left started by James Shea plucking a high ball out of the spring air and setting Justin away. LuaLua and Lee then combined to roll it into the midfielder's path 25 yards from goal, but this time his effort flew high over the bar.
LuaLua and Lee were revelling in the space down the right side of the home defence, but a couple more low centres went begging before Matty Pearson had to be alert at the other end to smother the attempts of Nichols to get to the left byline, winning a free-kick himself from referee Charles Breakspear in the process.
It was from that long ball forward by Shea that the second goal arrived. Collins brought the ball down and switched it left to Justin, ten yards inside the Rovers half. The left-back made his way towards the hosts' box and his 20-yard shot was deflected towards Lee, who laid it back for Berry to hammer his effort into the ground and into the bottom corner after a couple of bounces for his second goal in as many games.
Rovers were back in the game before half-time when Clarke-Harris cut in from the left touchline and in between Bradley and Pearson, before lifting his shot over the onrushing Shea.
The Hatters ought to have restored the two-goal advantage in the 52nd minute when Stacey skipped past his man again down the right, taking advantage of Michael Kelly's slip, and cut the ball back for Lee, but the ex-Barnsley forward's side-footed effort flew over the bar.
The hosts reverted to cynical means to halt the Hatters' attacking threat from then on, Shinnie, LuaLua and Berry all fouled within seconds of each other, as treatment for the former - who wasn't even awarded a free-kick for a late challenge on his knee by Abu Ogogo - caused a lengthy delay.
Thankfully the Scot was able to return to action, and Justin was the next to be thwarted by a late challenge from a Rovers defender - this time Ollie Clarke, the midfielder, the perpetrator.
The Hatters were furious with just over 20 minutes to go when Rovers centre-half Tony Craig took the ball from Collins' toe as the Town striker was about to play the ball back to Bonham at an uncontested drop-ball, after Berry had been down, and set the home side on the attack.
Bradley remonstrated with Craig as hosts prepared to take a free-kick won on the right as they looked to profit from the incident.
Eventually the Town cleared the ball, and Rovers midfielder Liam Sercombe became the first player into Breakspear's notepade for a trip on Mpanzu as the midfielder brought the ball away, and chance of any fluency returning to the half disappearing once again.
Rovers threatened in the 82nd minute when a cross from the right found its way to Clarke-Harris at the far post, but Stacey did well to get a block in to send it wide for a corner.
Harford brought George Thorne on in the 83rd minute for Berry to help stem the flow of home attacks, then George Moncur for Lee with two minutes left.
It proved effective as the Hatters managed six minutes of injury-time without a scare to seal a big three points in the bid to win promotion.
TOWN: Shea, Stacey, Pearson, Bradley ©, Justin, Mpanzu, Shinnie, Berry (Thorne 83), Lee, Collins, LuaLua (Cornick 74). Subs: Baptiste, Cornick, Moncur, Cummings, Sheehan, Isted.
Goals: Collins 17, Berry 39
ROVERS: Bonham, Lockyer ©, Craig, Upson, Sercombe, O Clarke, Nichols, J Clarke, Clarke-Harris, Ogogo (Reilly 83), Kelly. Subs: Smith, Jakubiak, Partington, Sinclair, Kilgour, Russe.
Goals: Clarke-Harris 45+2
Yellows: Sercombe 71
REFEREE: Charles Breakspear
ATT: 9,037 (1,145 Hatters)