Carlisle grabbed three points thanks to a second-half penalty from Irish striker Trevor Molloy.
Molloy sent Lincoln Keeper Alan Marriott the wrong way after defender Richard Logan was penalised for handling in his own area.
The goal broke the deadlock of a poor game played in stiffling heat.
Both teams struggled to string two passes together after being disrupted following a double sending-off after only eight minutes.
As the players prepared for a Carlisle free-kick the referee's attention was drawn to an incident on the edge of the Lincoln penalty area.
Then after a lengthy delay, Carlisle's Richie Foran was sent off along with Lincoln's Simon Weaver after each appeared to strike the other.
The game opened up after the penalty and Simon Yeo should have levelled things in the 77th minute but sent his shot straight at Carlisle's keeper Peter Keen.
By then Carlisle were down to nine men after Brian Shelley was dismissed for a foul on Yeo just 60 seconds earlier.
Lincoln, had a golden chance to equalise two minutes from time when Lee Maddison fouled Dean Cropper but Yeo hit the post with the penalty.
In stoppage time Molloy became the third Carlisle player to be sent off when he directed abuse at a linesman.
Afterwards, Carlisle's Maddison denied he had fouled Cropper for the penalty.
He said: "I never touched him. The referee gave everything to Lincoln. It's difficult enough playing with 11 men and we coped tremendously well. It was never a penalty.
But the referee made us want to prove something and we dug in deep."
Lincoln Manager Keith Alexander said: "The only decision the referee had to make was to send their man off when we won the penality but he even got that wrong. It was an absolutely diabolical performance by the official."