Mark Bailey's outrageous 80-yard last minute shot sealed the points for Lincoln and all but killed off Carlisle's hopes of yet another miraculous escape from relegation.
Bailey netted after Carlisle keeper Matty Glennon had ran forward for a last ditch free kick, but after a poor delivery a foul was awarded against the Cumbrian.
Standing 40 yards from his own goal, Bailey received the quickly taken free kick and lobbed his shot into the empty goal with Glennon stranded in the centre circle.
Earlier Carlisle had dominated, and but for a resilient Lincoln defence, would have surely created more chances to cancel out Peter Gain's classy 47th minute opener.
Good work from Gain and Sedgemore allowed Fletcher to flick the ball back to Gain who conjured an inch-perfect lob over Glennon from the edge of the box.
After that goal Carlisle pushed forward and despite working hard failed to create any clear chances, with only Andy Preece forcing visiting keeper Andy Marriott into a save.
A through ball from Peter Murphy found Preece in the box, but despite running away from goal he fired in a shot which would have nestled in the bottom corner had it not been for Marriott.
With the Cumbrians looking for an equaliser Lincoln hit back on the break and were unlucky to see Lee Andrews clear off the line after Gain's shot was only partially saved by Glennon.
Carlisle boss Paul Simpson admitted his disappointment after the game: "We didn't have enough about us today, their strikers had a little bit extra.
"But whilst there is still hope we will keep on battling, no one in that dressing room will jack it in." Lincoln boss Keith Alexander said: "We all worked hard, Andy Marriott's save from Preece was fantastic.
"We were excellent from start to finish today. It's a magnificent win under pressure, it's a hostile place to come to and our supporters were absolutely fantastic."