Eric Kinder's side left it late to clinch the win as goals from Jordan Slew and Hugo Fernandez sealed victory.
Academy striker Jordan Preston had set Rovers on their way with a smart finish in the first half but the experienced Aaron Mclean soon levelled.
The game appeared to be heading to extra-time and possibly penalties until Rovers won one of their own in the 89th minute when Slew was tripped in the box. He took the spot-kick himself and cooly slotted home.
The Tigers pushed forward for a late equaliser and Rovers were clinical on the break, Preston turning provider for Hugo Fernandez who chipped the advancing Hull goalkeeper to ensure cup progress.
Rovers welcomed back Tim Payne after injury, whilst Jordan Slew got another runout after recovering from a back injury, he was partnered in attack by Academy top scorer Jordan Preston.
In comparison, the Tigers had a stronger looking squad with experienced professionals Danny Graham, Aaron Mclean and Abdoulaye Faye included in their starting eleven.
At a chilly Leigh Sports Village the game was slow to get going, but when it did it was the visitors who fashioned the first opportunities.
Matthew Dixon and Danny Graham exchanged passes on the edge of the box before Dixon let fly but David Raya in the Rovers goal saved well with his legs.
Danny Graham's experienced strike partner Aaron Mclean was next to try his luck on 22 minutes when following a poor pass from Raheem Hanley the forward shot from distance but his speculative effort was over the bar.
Slowly Rovers grew into the game, full back Kellen Daly with a cross into the Hull box that saw New Zealand international Tim Payne arrive well to head goalwards but his effort was just off target.
Just before the half hour the deadlock was broken with Rovers taking the lead. Good pressure in and around the Tigers' area saw the ball eventually arrive at left winger Bradley Bauress, he fired the ball low across the area to the six-yard box where Jordan Preston fired home with a first time shot that went in off the far post.
It was the Scottish Under-19 international's 15th goal of the season, but his first at Under-21 level.
However Rovers couldn't hold onto their lead long as Hull City equalised on 32 minutes.
Rovers needed to be stronger defensively as the vistors worked the ball to Mclean and he squeezed the ball home from a tight angle.
A penalty shout for Rovers that went unheeded was the only further action as the first half ended all square.
Rovers started the second half with another penalty shout as Slew was brought down on the line. A free-kick was awarded which Bauress delivered from the right, Ryan Edwards nodded goalwards but Preston couldn't find the back of the net with an acrobatic shot on the turn.
The young forward would sting the gloves of goalkeeper Eldin Jakupovic on 54 minutes after a one-two with Jordan Slew, it was well struck but kept out.
The visitors responded with chances of their own, David Raya saving well to deny Danny Graham, but the well-travelled striker perhaps should have done better with the rebound as he poked wide.
Slack play from Rovers presented Hull with another chance as Aaron Mclean fed Graham once more but the forward steered his effort just beyond the far post.
Chances continued at either end with both sides pressing in an entertaining half, but on 88 minutes it looked as if it was the visitors who would progress when Danny Graham bore down on goal, he squared unselfishly for Mclean but David Raya pulled off a quite fantastic save to deny the striker.
It proved to be a pivotal moment as Rovers went up the other end and were awarded a penalty as Slew was upended.
He took the spot-kick himself and finished with a shot to the 'keeper's right.
Sixty seconds later and Rovers had confirmed their place in the last 16. With Hull pouring numbers forward, the home side hit them on the break, Jordan Preston teeing up Hugo Fernandez and he finished in style with a cool lob.
ROVERS: Raya, Daly, R. Hanley, Payne (sub Paulo Jorge 80 mins), Edwards, Tumwa, Fernandez, Lenihan (c), Slew, Preston, Bauress.
Subs not used: Haley, Urwin, Pero, Edinho.
Goals: Preston 28 mins, Slew (pen) 89 mins, Fernandez 90+1 mins.
HULL CITY: Jakupovic, Topliss, McElroy, Wilson, Clappison, Faye, Dixon, Armstrong, Graham, Mclean, Jahraldo-Martin (sub Fletcher 65 mins).
Subs not used: Watson, Barlow, Margetts, Chambers.
Goals: Mclean 32 mins.