Goals from Nathan Broadhead and Kieffer Moore sandwiched a Wes Harding own goal as Town secured a 3-0 half-time lead over Millwall at the Den.
Town boss Kieran McKenna, who was taking charge of the Blues for the 100th time in the league, made two changes with Cameron Burgess and Omari Hutchinson coming into the team and Conor Chaplin, for the first time in the Championship this season, and George Edmundson dropping out.
Burgess joined Luke Woolfenden at the heart of the defence with Edmundson left out of the 20-man squad and rested having played every game this year so far.
Hutchinson came into the three behind central striker Kieffer Moore along with Wes Burns on the right and Nathan Broadhead on the left.
Millwall handed starts to George Saville, Murray Wallace, Tom Bradshaw and Ryan Leonard with Joe Bryan out serving the first of a three-match ban handed out for violent conduct in Sunday’s 2-1 defeat at Coventry and on-loan Burnley striker Michael Obefemi was ill. Former Town keeper Bartosz Bialkowski was named among their subs.
The Lions struck the first shot of the game in the second minute. Leonard slamming Saville’s corner from the left over the bar after it had been played to him five yards outside the area.
Two minutes later, Hladky was forced to pat away a Saville shot which came through a crowd of players.
On 10, after a Town free-kick, Millwall broke through Bradshaw, but Harry Clarke did well to get back.
Moments later, a free-kick from the right was half-cleared to Leonard on the edge of the box and his powerful low shot was well saved by Hladky.
Millwall continued to look the more dangerous side and on 13 Hladky saved sharply at his right post from a Zian Flemming free-kick just outside the area to the left.
The Lions had started strongly, but the Blues began to take over as the game moved beyond the quarter-hour.
On 20, Leif Davis played a low free-kick to Broadhead on the penalty spot from the right and the Wales international swept a shot which clipped the bar on the way over, via a Millwall foot, the Town forward claimed, but referee Sam Barrott felt otherwise.
The Blues had begun to look the most likely scorers and in the 24th minute, they went in front. Following a corner needlessly conceded after Matija Sarkic, Wallace and skipper Jake Cooper miscommunicated, Hutchinson clipped the ball back in from the angle of the area on the right and Broadhead allowed the ball flick off the top of his head and into the far corner of the net, the Welshman’s 10th goal of the season.
Eight minutes later, it was 2-0. Broadhead was sent away down the left by Burgess and his cross was diverted into his own goal by Wes Harding, prompting boos from the sparse home support.
On 34, Town, who had been dominant since the first goal, might have made it 3-0 when Moore seized on an error by Harding midway inside the Millwall half but the defender did well to get back to slide in to take it away from the on-loan AFC Bournemouth man as he looked to shoot from the edge of the box.
The Blues continued to dominate and moments after the fourth official indicated four additional minutes, Clarke exchanged a one-two with Hutchinson on the right of the box, took it to the byline and stood up a cross for Moore, who headed his 50th Championship goal into the ground and into the top corner of the net.
The final whistle was greeted by loud boos from the home support, those that hadn’t already made their way to the bars.
Millwall had started strongly, as has often been the case of late, but Town took over around the 15-minute mark and dominated from there, making the most of Lions errors as they grabbed their three well-taken goals.
The Blues, previously having won only one of their previous nine, ought to see out the remainder of the game from here with little fanfare to move to within a point of third-placed Southampton.
Millwall: Sarkic, McNamara, Wallace, Cooper (c), Bradshaw, Flemming, Leonard, Saville, Esse, Honeyman, Harding. Subs: Bialkowski, Tanganga, Mitchell, Mayor, Campbell, Watmore, De Norre, Boateng, Walker.
Town: Hladky, Clarke, Woolfenden, Burgess, Davis, Morsy (c), Luongo, Burns, Broadhead, Hutchinson, Moore. Subs: Walton, Tuanzebe, Humphreys, Travis, Harness, Sarmiento, Chaplin, Jackson, Al-Hamadi. Referee: Sam Barrott (West Riding).