Nathan Tella netted in the opening minute for Burnley but George Hirst equalised two minutes later and the scoreline remains 1-1 at half-time.
Town boss Kieran McKenna named the expected much-changed side with only skipper Sam Morsy and centre-half George Edmundson starting from the team which began Saturday’s 1-1 draw at Cambridge United.
Vaclav Hladky started in goal with Janoi Donacien, Luke Woolfenden and Edmundson at the back.
Greg Leigh and Kayden Jackson were the widemen with Morsy, who can play despite having been booked twice earlier in the competition as one of those cards was prior to round three, and Cameron Humphreys in the middle of midfield.
The 19-year-old coming into the team was the only change from the side the Blues fielded in the 0-0 draw with the Clarets at Portman Road 10 days ago with Lee Evans having picked up a knock at the weekend. Sone Aluko and Marcus Harness were the number 10s behind central striker Hirst.
Town, wearing their all-black third kit for only the second time, named a strong bench but Harry Clarke was absent having been cup-tied, while Massimo Luongo and Wes Burns were also absent with manager Kieran McKenna having said at his morning press conference that "three or four” players hadn’t travelled due to knocks.
Burnley manager Vincent Kompany made seven changes from the team which won 3-0 at Norwich at the weekend and gave a first start to South African striker Lyle Foster, who made his debut as a sub in the game at Portman Road having joined the Clarets earlier in the month from Belgian side Westerlo.
The home side opened the scoring with the game less than a minute old. The Clarets carved their way through Town all too easily and Foster cut inside Edmundson in the area but the ball was knocked away from him and fell to Nathan Tella, who lashed into the roof of the net.
But the Clarets’ lead lasted only a minute. Aluko turned on halfway and played a ball down the right and Jackson out-paced Ian Maatsen before cutting back to Hirst, until recently was on loan with Burnley’s great rivals Blackburn, who bundled his first Town goal past Bailey Peacock-Farrell.
The top scorers in the Championship and League One respectively failed to find a goal between them in 90 minutes at Portman Road but managed two in three minutes at the second attempt.
On seven, Leigh forced an error on the Town left and eventually sent over a well-struck cross which flew behind the unmarked Jackson at the far post.
The game settled down after its frenetic start and Burnley began to pass the ball around with a slickness they rarely showed in the first match. On 18 Samuel Bastien unleashed a shot from 25 yards but was too close to Hladky.
In the 28th minute, the Clarets played themselves into trouble on the Town left and the ball was played to Leigh, who sent over a deep cross towards Jackson, which in the end looped over Peacock-Farrell’s bar with the keeper scrambling to get back.
A minute later, the home side gave the ball away again in their own half and Humphreys struck a shot from the edge of the box which deflected wide.
Town’s pressing continued to have an impact and just after the half hour, the Blues again forced the Clarets to give the ball away in their own half and Harness shot through to Peacock-Farrell.
Soon afterwards, Tella sent a dangerous ball across the Town area from the corner of the box on the right but just in front of Bastien.
In the 33rd minute, home skipper Jack Cork was shown the game’s first yellow card for a foul on Aluko on halfway, the veteran and his quick feet having given the Clarets more than a few problems and the travelling Town fans plenty to cheer during the first period.
Three minutes later, Hirst looped an effort wide after the ball had fallen to him in the area following a long throw from the right. On 38, Vitinho joined Cork in the book for a late tackle on Jackson.
Neither side was able to force a chance in three minutes of additional time and the half ended with Humphreys making a strong challenge which the home players and fans felt was a foul but in which referee Scott Oldham showed no interest.
Town could be more than happy with their first-half display. Having gone behind in the opening minute having been pull, Kieran McKenna’s side reacted superbly to level virtually from the restart, Hirst getting himself off the mark for his new club.
From there, Burnley had a spell when they started to look comfortable on the ball but Town quickly put an end to that, dispossessing or forcing errors in their own half on a number of occasions and having most of the game’s shots at goal even if Peacock-Farrell had been relatively untroubled by those efforts.
Burnley: Peacock-Farrell, Roberts, Al-Dakhil, Taylor, Maatsen, Cork (c), Bastien, Twine, Vitinho, Tella, Foster. Subs: Franchi, Beyer, Cullen, Brownhill, Churlinov, Zaroury, Dervisoglu, Gudmundsson, Barnes.
Town: Hladky, Donacien, Woolfenden, Edmundson, Jackson, Morsy (c), Humphreys, Leigh, Aluko, Harness, Hirst. Subs: Walton, Keogh, Davis, Ladapo, Chaplin, Burgess, Vincent-Young, Edwards, Broadhead. Referee: Scott Oldham (Poulton-Le-Fylde). Att: 11,543.