City without a win from their previous seven games produced a desperate first-half performance and were jeered off at half-time.
But manager Peter Jackson switched things around by bringing on substitutes Adrian Patulea, Ben Wright and Sam Mullarkey in a bid to pep up his team.
The switch paid off with Lincoln altering formation to 4-4-2 and over-running Stanley.
The equaliser came in the 68th minute when Aaron Brown crossed from the left. Wright saw his effort come back off Kenny Arthur and Patulea put the ball into the net from close range.
Patulea then hit the post with a low shot before Lincoln took the lead in the 78th minute.
Mullarkey crossed from the right and Brown was allowed to steal in from the far post to head home.
Brown was booked for his celebrations, but five minutes later he set up Lincoln's third goal when his cross was tapped in by Wright.
Accrington fell apart in stoppage time conceding two more goals. Mullarkey's hard work created a chance for Patulea who smashed a shot home for his sixth goal of the season.
The Romanian was involved again when he was brought down by Colin Murdock. Lee Frecklington sent the resulting penalty low into the bottom corner and Arthur was unable to keep it out.
The first half was a different story with Acrrington in complete control. They went ahead after 11 minutes when John Miles cut in from the left before lifting his shot over Rob Burch and into the top corner.
Miles caused Lincoln problems again in the 21st minute when his cross into the box caused chaos, before Lee Beevers eventually headed over his own bar.
Andrew Proctor was unlucky to have a scrambled effort disallowed for a foul.
But Accrington had three good chances in the closing minutes before the break. First Miles was sent clear but from a good position failed to find the net.
Then Gregg Blundell set up Jamie Clarke whose low shot was deflected past Burch, only for Daniel Hone to clear off the line.
With Lincoln reeling Miles fired another cross into the box. Proctor got between two defenders, but with a goal at his mercy failed to hit the target.