Jason Roberts had given the visitors the lead early in the second half, but Kuqi's 84th minute equaliser left Rovers still in the hunt for fourth place, much to Paul Jewels disbelief.
Mark Hughes made two changes to the side that defeated Sunderland at the weekend, David Bentley preferred to Brett Emerton on their right and Robbie Savage returned from suspension to replace Tugay.
Wigan were forced into one change following their 2-1 defeat at home to West Ham, with Henri Camara missing for family reasons, Andreas Johansson partnered Roberts in attack.
Steven Reid was involved in the thick of the action early on, almost connecting with Paul Dickov's cross on two minutes, before firing over the top into the Darwen End stand with a strike from 25 yards.
In a frantic four-minute spell towards the end of the first half, both sides had chances to take the lead.
On 33 minutes Johansson pulled the ball back to the unmarked Graham Kavanagh, who fired high and wide, before Morten Gamst Pedersen twice went close for the home side.
The Norwegian's low free-kick through the wall was well saved by the unsighted John Filan.
However, the Aussie keeper then handed Pedersen an open goal, only for referee Phil Dowd to award what looked like a harsh foul against Dickov.
But just minutes before the break, the Latics too had a goal struck off. A free-kick into the box was blasted home by Arjan De Zeeuw, only for the linesman on the far side to raise his flag.
Eight minutes into the second half however the visitors did take the lead. Lee McCulloch's crisp strike produced a brilliant reaction save from Brad Friedel, but from the resulting corner, Pascal Chimbonda headed goalwards and Roberts flicked ball into the net from two yards.
As Rovers pushed for an equaliser, Craig Bellamy was the surprise source of missed opportunities, glancing two free headers wide of the post.
But with just 6 minutes remaining, Rovers' sustained pressured paid off.
Ex-Rover Filan failed to hold on to Reid's ball into the area under pressure from Lucas Neill and Kuqi was on hand to slot the ball home for a deserved point.