The Imps continued to push for a winner, finding it through forgotten man Melbourne, gaining the three points that could prove crucial come the end of the season.
Story of the match
The opening chance fell the way of the home side, as Jephcott saw an effort saved by young keeper Sam Long after seven minutes.
Marquis then fired over Lincoln's first attempt from the edge of the box, as he looked to impose himself on the game.
Long was then called into action again, pulling off a good save from distance to deny Ryan Broom.
Arriving to meet Niall Ennis' cross, Jephcott made no mistake, smashing the ball in to give Argyle a deserved lead.
The Imps rallied in the final ten minutes of the half, with the best chance being when Whittaker saw his cross deflected onto the post, but ultimately found themselves behind at the break.
However, Lincoln came out swinging in the second half and found an equaliser through Marquis' close range finish, shifting the balance back in their favour.
The away side then saw several efforts blocked, before a last gasp challenge from former Imp James Wilson denied Marquis as he found himself one-on-one.
Long was on hand to save Joe Edward's strike from distance, as Plymouth looked to forced the momentum back in their favour.
A scrappy period followed as we entered the latter stages of the game, which was ended when Adam Randall saw a free-kick brilliantly saved by Long with ten minutes remaining.
The game looked to be heading for a draw, but Melbourne found the back of the net from a corner to earn Lincoln the win and make the long journey worth it.
Plymouth let down by final third as promotion chase takes another hit
The Pilgrims were looking to recover from their disappointing defeat to Sheffield Wednesday last time out, and a home game against a side in 18th looked the perfect opportunity.
A 1-0 lead at the break is certainly something you'd take, but they would have wanted to have been further ahead considering the chances created and positions they found themselves in.
And once Lincoln had pegged them back, they didn't seem to have an answer, struggling to carve out any clear-cut opportunities before the game was then lost. Leaving Steven Schumacher to pick his players up ahead of a big game against Fleetwood Town in midweek.
Appleton's new signings show promise as Long shines as deputy
City have had a busy week in the transfer market, with three more new arrivals coming in the door to hopefully make a positive impact on the pitch.
And one of them did just that, as Marquis was involved heavily and managed to get his name on the scoresheet. He came with criticism from his previous club Portsmouth, but with performances like that, he'll no doubt be a good signing.
Michael Appleton will have also learned that in youngster Long, he has a goalkeeper that he can rely on for the club's long-term future.
Man of the match
On-loan goalkeeper Josh Griffiths had a scan this week which showed an injury, causing him to miss his first league game of the season. Which allowed 19-year-old Long to make his league debut.
He was brilliant from start to finish, making important saves from Jephcott, Broom and Randall to keep his side in it, giving his manager reason to put his faith in him much more often.