A Chris Wood goal six minutes from time saw Rovers crash out of the EFL Cup at the third round stage.
With extra-time looming, the New Zealand international scored the only goal of the game, reacting quickest to head home after David Raya had saved his initial effort.
The first half was notable for stunning saves from long-range strikes. Raya denying Lewie Coyle at one end, Marco Silvestri keeping out a thunderous effort from Jack Byrne at the other.
Play opened up in the second half with chances for either side. Rovers were denied by a double save to keep out Marvin Emnes and Elliott Bennett, whilst Raya saved efforts from Pablo Hernandez and Kemar Roofe.
But just as it looked like an additional thirty minutes would be required, the home side struck the decisive blow thanks to Wood's close-range header.
Rovers pressed to the end and as Emnes pulled the ball back for Hope Akpan inside the area the midfielder was caught as he was set to shoot, but as the referee waved away their appeals, with it went the chance of the Lancashire club reaching the fourth round.
As expected, Rovers made nine changes for the club clash with Leeds, just captain Jason Lowe and striker Sam Gallagher retaining their places from Saturday.
David Raya was one of those returning to the starting XI and the young Spaniard was called into action inside the first minute at Elland Road.
The home side pressured from the off and after Lowe had blocked a shot from Roofe the ball ran out to full back Coyle who unleashed a stupendous effort that was only matched by Raya's flying save.
Martin Samuelsen, making his first start, then drove at the Leeds defence to feed Bennett, his deep cross picked out Liam Feeney at the back post but his header brushed the side-netting as the ball flashed the wrong side of the upright.
But having made wholesale changes before kick-off, Rovers were then forced into another as Scott Wharton pulled up. Unable to continue it meant a second senior appearance for Ryan Nyambe.
That lead to a makeshift back four of Lowe, Nyambe, Darragh Lenihan and Stephen Hendrie, yet it was Scottish defender Hendrie who would have the next opportunity in front of goal.
On 16 minutes both Sam Gallagher and Samuelsen won important headers in the area, the ball dropped to Hendrie outside the box but his right-footed half-volley bounced side.
Play settled down after that early flurry of chances, but as the first half headed towards it's goalless conclusion it was Rovers with the pressure once more.
After Bennett saw a shot deflect wide, the resulting corner kick came out to Byrne who struck sweetly from outside of the box, the ball seemed to be arrowing towards the top corner until Silvestri pulled of a save that was every bit as good as Raya's one minute into the match.
Roofe flashed a shot just wide for Leeds early in the second half but that was a rare effort at goal in a quiet first 15 minutes after the restart.
The home side made their first change with Pablo Hernandez replacing Ronaldo Vieira, whilst Rovers completed their substitutions as Connor Mahoney and Marvin Emnes replaced Samuelsen and Gallagher.
Almost immediately the Dutchman was involved in front of goal, latching onto a high ball from Hendrie, Emnes shot goalwards but Silvestri saved. The keeper then failed to get a meaningful touch on his attempted punch but then redeemed himself by keeping out Bennett's goalbound effort.
The resulting corner saw Rovers threaten once more. Feeney in from the right, Bennett with the acrobatics, but the ball only found the side-netting.
However in the closing stages it was the home side who built up a head of steam that would culminate in them finally breaking Rovers' resolve, grabbing the winner six minutes from time.
After Raya had claimed a header from Roofe and tipped aside a free-kick from Hernandez, the Spaniard was finally beaten in the 84th minute.
With the Rovers backing off Hernandez let fly, Raya did well to push the effort aside, but as Roofe drilled the ball back across the six-yard box, substitute Wood poked goalwards, Raya flung himself to the right to make the save, but in keeping the ball out it rebounded back off the Kiwi and into the back of the net.
Unbowed, Rovers pressed until the end, and saw strong claims for a penalty waved away in the third of four added minutes at the end of the game.
Mahoney showed quick feet and good awareness to find Emnes in the box but as he teed up Akpan for the shot he appeared to be clipped from behind, Leeds eventually hacking the ball clear as Rovers' appeals went unheard.
A last-gasp corner saw David Raya join the attacking Rovers ranks, but the home side cleared their lines to ensure it would be the Yorkshire outfit that would progress through to the fourth round.
LEEDS: Silvestri, Phillips, O'Kane, Roofe, Antonsson (sub Wood 71 mins), Bartley, Coyle, Mowatt (sub Grimes 83 mins), Taylor, Cooper (c), Vieira (sub Hernandez 58 mins).
Subs not used: Green (GK), Ayling, Dallas, Denton.
Goals: Wood 84 mins.
Booked: Phillips 29 mins.
ROVERS: Raya, Lowe, Lenihan, Wharton (sub Nyambe 8 mins), Hendrie, Feeney, Akpan, Byrne, Bennett, Samuelsen (sub Mahoney 62 mins), Gallagher (sub Emnes 62 mins).
Subs not used: Steele (GK), Marshall, Guthrie, Conway.
Booked: Akpan 11 mins, Lenihan 79 mins, Emnes 90 mins.