City's run in the Vertu Trophy came to an end - with former Imp Joe Taylor having the decisive impact in a tight encounter with Huddersfield Town.
Taylor, who struck 10 goals for City while on loan in 2023/24 - struck from close range early in the second half before Murray Wallace added gloss to the scoreline with a header in time added on.
Head coach Michael Skubala made nine changes to the squad who earned all three points against Port Vale in League One on Saturday. Goalscorer Reeco Hackett retained his place with Tom Hamer, while Ivan Varfolomeev and Dexter Lembikisa were among the players coming into the line-up.
Skubala was forced into an early change with Freddie Draper coming on for the injured James Collins, and Hamer taking on the captain’s armband.
City's first chance came after 22 minutes. Draper took a free-kick quickly after his counter-attack was cynically stopped and Reeco Hackett did well to beat a man before his cross was blocked for a corner. Hackett took the subsequent corner, and it nearly went in directly but for a defensive clearance at the back post from Wallace.
After 25 minutes the visitors earned a free-kick, no further than 20-yards out, and the responsibility fell to the former City man Sean Roughan - the Terriers left-back managed to fire the set-piece on target but it was saved well by Zach Jeacock.
After 30 minutes the Imps had their best chance of the game so far when Draper was fouled for the second time in the short period he had been on the pitch. Hackett was the designated taker of the free-kick, which was positioned just outside the Terriers’ box, and he hit the target but Lee Nicholls was perfectly placed to collect.
Taylor brought a fine left-handed diving save out of Jeacock after being set up by Marcus Harness.
Nicholls pulled off an impressive reflect save to keep the score level at the interval. Some good work from Lembikisa earned the Imps a dangerously placed throw in which was hurled in by Hamer and met at the near post by Rob Street - the ball found its way through the crowd to Draper’s feet, and he could only find the glove of the visiting keeper.
The decisive moment of the match came four minutes into the second period. Roughan's free-kick from the right was deep and met by the head of Alfie May - he knocked the ball back into the six-yard box and Taylor poked the ball home.
Jeacock was called into action again after 57 minutes when May got a series of shots away in quick succession - three in total.
Skubala sent on reinforcements to try and find a way back into the game. Moylan almost had an instant impact with a rifled shot which was well held by Nicholls.
The Imps had a chance to equalise with less than five minutes left on the clock when Hackett swung in a dangerous corner which found Moylan at the back post and Frankie Okoronkwo saw his shot blocked by a team-mate before lifting the rebound over.
And in the closing stages of the match Wallace rose highest to head home the second goal of the game and season the visitors' spot in the round of 16.
Imps: Jeacock, Towler, Hackett, Bayliss, Collins (Draper, 17), Ring (Moylan, 62), Jefferies (Darikwa, 62), Street, Hamer, Lembikisa (Bradley, 78), Varfolomeev (Okoronkwo, 78). Unused Subs: Wickens, Barbrook.
Huddersfield Town: Nicholls, Sorensen, Wallace, Low, Wiles, Taylor (Radulovic, 88), Harness, Kasumu (Vost, 71), Roughan, May (Charles, 82), Ashia (Rooksen, 71). Unused Subs: Goodman, Balker, Castledine.
Attendance: 2,016 (211 away)
Referee: Ben Speedie