Kevin McDonald's late strike earned all three points for the Grecians after an entralling game at the LNER Stadium.
After a closely fought first half, City mounted a late attack in stoppage time after a well-defended second half. A shot from Kevin McDonald on the edge of the box in the 94th minute proved fatal for the high-flying Imps, with the Grecians holding on to claim their fourth win of the season.
Gary Caldwell opted for just one change to the side that lost 0-1 at SJP to Huddersfield Town, with Johnly Yfeko making his first league start since October 2024 in the place of Jake Doyle-Hayes who missed out due to injury.
First Half
It was a slightly slow start to the game as both sides looked to test out the opposition, but it was the Grecians who had the early opportunities.
Reece Cole whipped a teasing ball from the left wing into Josh Magennis and Jayden Wareham but neither forward was able to get a goal-ward touch.
Minutes laters, Magennis had the first shot of the game, capitalising on a poor defensive header but sending his powerful low shot wide from distance.
Lincoln started to gather stock and forced Magennis into a brilliant headed clearance from close distance to deny James Collins in the 15th minute.

The action fizzled out slightly towards half-time, with a free-kick from Cole, which curled wide of George Wickens' near post, the only major action before the referee's first whistle.
Second Half
The hosts wasted no time in applying the pressure after the break, with a shot from Draper clattering the far post of a relieved Whitworth, before Sweeney was able to clear the away from danger.
City's first attempt of the second half came in the form of an ambitious effort from Danny Andrew, who's shot rose high and wide of the Lincoln goal.
A resilient display of defending from the Grecian's would soon follow, with Whitworth combining with the defensive back line to produce a series of impressive shots and blocks after a dangerous counter-attack from the Imps.
McMillan produced a fine cross into the Lincoln box on the hour mark, with Magennis not quite able to reach it and Lincoln clearing, before falling to Cole, whose shot was blocked.
With ten minutes left on the clock, another scramble inside the City box would ensue. A series of blocked shots would finally curtail, as Whitworth confidently claimed the ball.
A total of nine additional minutes were added on, with City withstanding pressure from the hosts, before mounting a counter attack in the 94th minute.
A strike from Kevin McDonald on the edge of the box found its way into the Lincoln goal, igniting a party in the away end. The Grecian's held on until the referee's whistle, claiming a fourth win of the season.

Up Next: City are back at SJP next weekend where we face Reading, make sure to come along as we go for two wins in two! Get your tickets here.
Lincoln City: Wickens, Darikwa (C)(Hamer 78'), Reach, Jackson, Bayliss, Collins (Hackett 68'), Bradley, Street (Obikwu 78'), House (Ring 87'), Varfolomeev, Draper.
Subs not used: Jeacock, Towler, Ring, Okoronkwo.
Exeter City: Whitworth, McMillan, Fitzwater, Brierley, Wareham (McDonald 82', Cole (Aitchison 82'), Niskanen, Yfeko (Higgins 62'), Andrew (Turns 89'), Sweeney (C), Magennis.
Subs not used: Bycroft, Woodhouse, Wilson.
Goal: McDonald 90+4'
Yellow cards: Whitworth 15', Brierley 90+11'
Attendance: 9,053 (251 away)