Lincoln twice came from two goals behind in an astonishing clash at Craven Cottage as Keith Alexander's men produced a fantastic performance.
Fulham boss Chris Coleman changed his entire side from Saturday's 2-1 defeat to West Ham. Heidar Helguson, Ricardo Batista, Philippe Christanval and Ahmad Elrich all made their first-team debuts.
Lincoln looked good from the start as they created a chance straight from kick-off. The ball fell to striker Maheta Molango on the edge of the penalty area but his effort drifted over the crossbar.
The Red Imps were presented with another chance on eight minutes but Molango fired a shot into the sidenetting.
Eventually the Premiership outfit took hold of the game and Christanval hit their first shot at goal over the bar on 15 minutes.
Before long Fulham broke the deadlock. Collins John flicked the ball wide to Helguson on the right and his cross was met by the head of Zesh Rehman, who planted the ball in the bottom corner.
On 31 minutes things got worse for the visitors, as the Whites added a second. Goalkeeper Alan Marriott made a fantastic point-blank save from a John drive, but Helguson was on hand to nod home.
In the second half the Imps turned up the tempo and tried to snatch an early goal to put their hosts on the back foot.
Molango fired a shot into the arms of keeper Batista on 52 minutes, before he had another shot deflected wide by Dean Leacock on the hour mark.
Francis Green went close again moments later and eventually Lincoln got themselves a lifeline through the striker. Gary Birch carved through the defence before picking out Green who drilled a shot into the far corner on 70 minutes.
McBride missed two good chances to kill the game off, before Moritz Volz miskicked on 81 minutes to put the ball past his own keeper. He had only come on as a substitute moments earlier.
Lincoln's Birch and Fulham's Tomasz Radzinski both had chances in the dying seconds.
Extra-time was just as entertaining - as once again Fulham threw away a two-goal lead. Three minutes in Liam Rosenior rose to head past Marriott from Green's corner and soon after Radzinski slid the ball home for number four.
Scott Kerr hit a brilliant free-kick on 100 minutes to make it 4-3 and there was more drama as Marvin Robinson bundled the ball home six minutes from the end.
But it was a cruel end for Lincoln as McBride headed home from a deep Adam Green free-kick to win the game.