Leading goalscorer Carlton Morris struck on the stroke of half-time to make it 18 goals for the season, before Cauley Woodrow added a second soon after the break to extend the Town's unbeaten run to ten matches and lift them back above Middlesbrough on 74 points.
Manager Rob Edwards made two enforced changes, with captain Sonny Bradley returning from the start for the first time since November 1st, when he suffered a knee injury against Reading.
Also in from the kick-off was Woodrow, partnering Morris up front, as Alfie Doughty and Elijah Adebayo missed out through injury having gone off in the 3-1 win over Blackpool on Easter Monday.
The Hatters kicked-off in fourth place following Boro's 5-1 Friday night win over Norwich, unbeaten in nine matches overall and on a nine-game undefeated run on the road, too.
Rotherham were in good form themselves, unbeaten in three and 18th in the table, four points above the relegation zone.
After a feisty opening few minutes, with Morris and Rotherham centre-half Cameron Humphreys spoken to by referee Leigh Doughty following an altercation by the corner flag, the Hatters made the early running.
Mpanzu saw a shot blocked in the area, while his sidekick Campbell was latching onto every loose ball in midfield and probing to create an opening for top scorer Morris.
The Millers tried to make inroads down the side of the Hatters' new-look back three, with Reece Burke and Tom Lockyer either side of Bradley, but Ethan Horvath was equal to Jordan Hugill's low cross from the right and Chiedozie Ogbene over-hit his from the left.
Morris saw an attempted curler blocked by Conor Coventry on 23 minutes before Lockyer tried his luck in the 26th, although his 25-yard shot was only troubling the home fans behind the goal.
Rotherham midfielder Leo Hjelde was first into ref Doughty's book for a foul on Drameh, and he was soon joined by Reece Burke for pulling back Ogbene.
Morris headed onto the roof of the Millers' net from Woodrow's clever cross five minutes before half-time, then Ogbene sliced a shot wide at the other end while off balance, under pressure from Marvelous Nakamba.
Rotherham keeper Josh Vickers made a brilliant save to deny Amari'i Bell a 43rd-minute opener after a lung-bursting run to the byline by Cody Drameh, but the breakthrough wasn't long in arriving.
The Hatters maintained the pressure and kept the hosts penned in their own box, with Bell sending in a deep cross that Tyler Blackett could only flick to the feet of Morris well beyond the far post.
The ex-Millers loanee, who had been booed continuously following the early exchange with Humphreys, chopped back onto his left foot and curled into the top corner for his 18th goal of the season, and the perfect chance to silence the crowd.
Town were two goals to the good within a couple of minutes of the restart, after ref Doughty rightly penalised Rotherham defender Wes Harding for handball as he looked to shepherd Drameh's spinning cross out for a goal-kick.
Woodrow stepped up to take the penalty, which was saved by Vickers but the Town forward was first to react, steering home the rebound for his third goal of the season.
Morris came close again on 56 minutes, volleying Bradley's knock-down from Drameh's corner into the side-netting, but after the Hatters had survived an appeal for a penalty for handball as Jamie Lindsay fired a shot in from 25 yards, the striker was substituted in the 67th minute after receiving treatment for a knock, with Joe Taylor coming on in his place.
Mpanzu was soon trying to add a third, curling over from Woodrow's clever lay-off, then sub Luke Berry - on for Woodrow - was denied by a block as he looked to finish off a flowing move that had seen Drameh and Mpanzu raiding down the right.
Berry had the ball in the net a couple of minutes later, only for an offside flag to rule it out, then Bradley saw an 81st-minute header from Drameh's right-wing corner saved by Vickers.
Town's immense backline was depleted with Burke going off with a knock on 86 minutes, with Mpanzu dropping into right-sided centre-half and Luke Freeman on in midfield.
But with skipper Bradley and Lockyer both immense, as Burke had been alongside them, a 19th clean sheet of the campaign was secured in Ethan Horvath's quest for the golden glove, the only goals from open play the Hatters having conceded in the last 15 games coming in the 2-2 home draw with Millwall on February 28th and the one against Blackpool.
Now focus turns to the trip to Reading on Wednesday night and the chance to cement a place in the play-offs for the second season in a row.
TOWN: Horvath, Drameh, Burke (Freeman 86'), Lockyer, Bradley (C), Bell, Nakamba, Mpanzu, Campbell, Morris (Taylor 66'), Woodrow (Berry 70').
Subs: Shea, Lansbury, Watson, Thorpe.
Goals: Morris 45', Woodrow 47'
MILLERS: Vickers, Harding, Coventry (Rathbone 52'), Fosu (Wood 68'), Hugill (C), Ogbene, Lindsay, Peltier (Bramall 58'), Humphreys, Hjelde (Quina 52'), Blackett (Kelly 68').
Subs: Hemfrey (GK), Odoffin.
Att: 11,009 (2,125 Hatters)
REFEREE: Leigh Doughty