Callum Wright started where he left off at the end of 2019/20, breaking the deadlock early in the second-half, before Keane Lewis-Potter levelled the scores.
But there was late drama as George Hirst netted a penalty deep into added time, to secure a perfect start for the Foxes in the EFL Trophy.
City, one of the invited Premier League teams to take part in the competition alongside Sky Bet League 1 and League 2 clubs, were playing their first competitive fixture since a 3-1 away victory over Southampton in Premier League 2 Division 1 in March - when Wright and Hirst were the goalscorers.
Bidding to reach the knockout stages of the competition for a second successive season, the Foxes began in a 4-3-2-1 formation with Ali Reghba and Tyrese Shade sitting just behind lone forward Hirst.
Leicester's youthful squad was matched by The Tigers, who handed out five senior debuts.
The visitors started on the front foot, with Shade laying off Callum Hulme to send a powerful strike towards goal, only for Harvey Cartwright's diving save to deny City the perfect start inside the opening minute.
In a first half an hour devoid of clear-cut chances, Wright took aim from 20 yards out, but the midfielder couldn't find the target, seeing his shot sail over the bar.
Just under 10 minutes from the break a lapse in concentration from Cartwright, passing the ball straight out to Hirst, almost got City's striker off the mark for the season, but for a recovery save from Hull's keeper.
Hull then created their first real chance of the game when Lewis-Potter twisted and turned on the edge of the area to create an opening, but saw Jakub Stolarczyk hold on to his effort.
Back at the other end, Layton Ndukwu whipped in a dangerous in-swinging corner that captain Sam Hughes almost turned in from close range, while James Berry failed to trouble Foxes stopper Stolarczyk with his curling effort.
The ball dropped for Reghba inside the six-yard box but he was unable to make any meaningful contact and Cartwright smothered the ball, in what was the final action of the first-half.
City also started the second period on the front foot, as Hirst rose highest to meet Shade's looping cross, only to head narrowly wide of the far post.
And the away side took the lead five minutes after the break - Ndukwu's inch-perfect free-kick from the right was headed home by Wright, to open his account for the season.
Hull were close to responding immediately when Sean McLoughlin's flicked effort had to be cleared off the line by Mitch Clark, before Callum Jones' header forced Stolarczyk to punch the ball away from the resulting corner.
Jacob Greaves headed wide from Martin Samuelsen's cross as the Tigers continued to press for an equaliser.
City's youngsters still carried a threat, however, and Ndukwu's powerful long-range effort was only parried by Cartwright, into the path of the onrushing Reghba, but City's shot-stopper recovered to thwart the Leicester man from close range.
Hull's first change of the game paid dividends as substitute Billy Chadwick crossed for the unmarked Lewis-Potter to head home from inside the box shortly after coming on.
As the game entered the closing stages, Hulme's free-kick was close to finding Hughes at the back post, only for a late intervention denying Leicester the winner.
Chadwick's cross then forced substitute Terell Pennant to get back and clear the danger, before the City youngster went up the other end and shot narrowly wide of the near post.
But the winner came when Will Russ was hauled down in the area and the referee pointed to the spot. Hirst stepped up and, despite Cartwright going the right way, he confidently slotted the ball into the bottom corner.
Young forward George Hirst remains cool to convert a late spot-kick for the Foxes.
Callum Wright's diving header gave City the lead, but it was a late spot-kick, coolly converted by George Hirst, that ultimately won the game in dramatic circumstances right at the end and ensured three points headed back to Leicester.
Layton Ndukwu was a threat throughout the game in East Yorkshire.
Midfielder Layton Ndukwu cut a composed figure in the middle of the park, dictating play from deep and getting forward to join in with attacks, whilst also assisting the goal with a delightful set-piece delivery, before moving out onto the left in the closing stages.
Where does it leave us?
Coach Steve Beaglehole congratulates his players at full-time at KCOM Stadium.
City's youngsters are top of Group H on three points, with Hull in fourth, yet to get off the mark.
Elsewhere in Group H, Grimsby Town host Harrogate Town later this evening as both sides' campaigns get underway.
Callum Wright and George Hirst
The opener came via a brave Callum Wright header in the early stages of the second half.
City’s youngsters travel to face Harrogate Town in their second EFL Trophy group game on Tuesday 6 October (7:45pm BST kick-off). You will be able to follow live coverage of the clash on LCFC social channels.
City: Stolarczyk, Clark, O’Connor, Hughes (C), Flynn, Ndukwu, Hulme, Wright, Shade (Pennant 66'), Reghba (Russ 72'), Hirst.
Subs not used: Doherty, Nelson, Godsmark-Ford, Maswanhise.
Goals: Wright 50’, Hirst (pen) 90+4'.
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