Martyn Waghorn scored twice and Joe Garner once as Town ended a remarkable first half 3-2 in front at Millwall having gone behind in the opening minute, Jed Wallace and Aiden O’Brien having scored the goals for the home side.
Mick McCarthy named the expected side with all four of his frontline strikers starting. David McGoldrick partnered Garner up front with Waghorn on the right and Freddie Sears on the left.
Flynn Downes travelled having suffered knocks at Barnsley on Saturday but wasn’t in the 18 with Grant Ward alongside Cole Skuse in the middle of midfield.
At the back, Jordan Spence joined skipper Luke Chambers at centre-half with Dominic Iorfa at right-back and Jonas Knudsen on the left. Bartosz Bialkowski was in goal.
Bersant Celina missed out as he is again unwell, while Michael Crowe is the sub keeper with Dean Gerken missing the trip for personal reasons.
With 10 first-team players currently unavailable - Celina, Gerken, Downes, Tommy Smith, Adam Webster, Teddy Bishop, Tom Adeyemi, Luke Hyam, Andre Dozzell and Emyr Huws - Town named a very inexperienced bench with Myles Kenlock having made the largest number senior appearances for the Blues.
Millwall took the lead with the game’s first attack in the 44th second. O’Brien crossed from the left, Knudsen challenged with Steve Morison and the ball dropped for Jed Wallace eight yards out. The former Pompey man was able to wait for it to bounce before hitting a shot which appeared to catch two Town defenders on its way past Bialkowski and into the net.
Millwall’s lead lasted only three minutes. After receiving the ball from Iorfa midway inside the Lions' half Garner struck what looked like a speculative shot from almost 30 yards out which deflected off Shaun Hutchinson and wrong-footed Jordan Archer in the Millwall goal, who dived beyond the ball as it flew past him to his left.
The game continued to be an end-to-end affair, Ward eventually clearing after a minor scramble in the Town box.
On 12 O’Brien turned the ball over the bar when well-placed 10 yards out, the ball having broken to him from the right. The Irish U21 international will feel he ought to have done better.
Ward picked up the game’s first yellow card in the 24th minute for a high boot as he challenged Shaun Williams on halfway.
A minute later, Iorfa blocked a powerful George Saville shot from just outside the area with the Lions having most of the ball and looking the more dangerous of the sides.
On 28 Shaun Hutchinson headed Williams’s freekick from the left over the bar at the far post, Iorfa having fouled James Meredith.
The Millwall left-back was booked a minute later for an obvious dive as he chased a return pass into the area.
Having rarely threatened since their equaliser, the Blues took the lead in the 34th minute. Garner picked up the ball from a loose Saville throw on the Blues’ left and fed the overlapping Ward.
The former Spurs man whipped over a low ball which Waghorn slammed into the net at the near post having run across Hutchinson.
But as with Millwall’s earlier lead, Town’s advantage wasn’t to last too long. Two minutes had past when Bialkowski saved Lee Gregory’s shot down to his left and then scooped the loose ball away when grounded when it appeared a couple of his defenders might have been in a position to put it behind.
Saville subsequently struck a shot from a tight angle on the right which hit the bar and bounced down to O’Brien, who looped goalwards with Spence only able to slam into the roof of the net as he sought to clear.
What had started as an open game had become even more open with both teams looking likely to score every time they went forward. On 37 Garner whipped over a cross from the left which Waghorn just failed to reach.
In injury time Knudsen crossed from the left and Waghorn headed wide at the far post but in the final moments of the half the last week’s signing from Rangers gave the Blues the lead for the second time, via a goal which was mainly down to the skill and persistence of McGoldrick.
The Irish international looked second best to reach Garner’s pass into his path on the right of the area but beat Meredith for strength, then put the ball to one side of Hutchinson and ran the other and took it away from the keeper, before cutting it back to Waghorn, who turned in his third goal for his new club.
Referee James Linington ended what had been a pulsating half soon afterwards with the Town support still cheering the goal.
At times the period had resembled a basketball match with one side scoring at one and and the other doing the same at the other.
Town boss Mick McCarthy will have been delighted with the quality of his attackers’ creativity and goals but equally unhappy and frustrated by the manner in which his makeshift defence had conceded. Millwall manager Neil Harris will have felt much the same. Further goals after the break at both ends appear a certainty.
Millwall: Archer, McLaughlin, Hutchinson, Webster, Meredith, Wallace, Saville, Williams, O’Brien, Morison (c), Gregory. Subs: King, Craig, Thompson, Onyedinma, Ferguson, Elliott, Cooper.
Town: Bialkowski, Iorfa, Spence, Chambers (c), Knudsen, Skuse, Ward, Waghorn, Sears, McGoldrick, Garner. Subs: Crowe, Rowe, Nydam, Kenlock, Morris, McDonnell. Referee: James Linington (Newport, Isle of Wight).