Boulding's 16th goal of the season had given Stags the lead four minutes into the second half only for Jamie Forrester levelled 11 minutes later from the penalty spot.
But Stags were dominant in the last 20 minutes and Boulding, so impressive against Middlesbrough on Saturday, stole a deserved late, late winner for an amazing third successive away win.
Mansfield keeper Carl Muggleton had made a superb save inside the opening 90 seconds as Lincoln put the visitors under heavy pressure for 25 minutes.
But he only had one more real stop to make as Stags had much the better of the chances on the night and both Boulding and new boy Will Atkinson came close while Ian Holmes twice almost found a winner in the last nine minutes, hitting the bar before Boulding struck with goal number 17 of the season.
Stags' starting line-up was unchanged for the third successive game which meant new loan signing Atkinson had to be content with starting on the bench.
Proceedings began with a minute's silence for former Imps chairman Frank Eccleshare.
City kicked off in heavy drizzle but Stags were first to threaten as Marriott left his area to head clear Bell's long through ball.
However, Muggleton made a crucial save inside 90 seconds as sloppy Mansfield passing saw John-Lewis burst through the centre and found himself one on one with the keeper, Muggleton spreading himself well to block the low finish.
There was more worry for the visitors when they struggled to clear Marriott's long free kick and it bounced dangerously across the box.
Green got in another important interception, his head preventing Brown's cross field ball finding D'Laryea in space on the left.
On 17 minutes Lincoln came very close as John-Lewis' run set up Dodds on the left of the box and he rolled a finish across Mugleton and wide of the far post.
Soon after Brown was not too far over with a long range blast as the home side continued to dominate.
Kerr bundled a shot wide from 18 yards from a poor clearance before Stags finally had sight of the home goal on 26 minutes as Boulding lifted a 20-yard half volley wide of the far post.
Bell's pass into the left of the box offered Brown a run but he was soon crowded out after delaying a shot and his cross came back to him and straight off his head for a goal kick.
On the half hour Martin's lofted pass was controlled in the box by Boulding and he saw his shot on the turn deflect for a corner which reached Buxton who sent a tame header wide.
Boulding tried to touch Hamshaw's cross into the path of Dawson in the box only for Ridley to get in a crucial touch as he shaped to shoot and again the corner was easily cleared.
Kerr pulled a low corner back to Forrester in a well worked routine which saw the Imps hitman's first time finish deflect wide for a second corner.
Beevers got his head onto the end of a Green free kick on 43 minutes, but again Muggleton was there to turn the ball over his crossbar.
Mansfield were caught cold on the restart as Forrester was sent clean through within the first 30 seconds. However, the chasing Jelleyman timed his tackle to absolute perfection and Forrester and the home fans' protestations go them nowhere.
The sides exchanged corners before Stags broke through on 49 minutes. Hamshaw ran at the home defence and then squared to Boulding on the right of the box. He cut inside and drilled a low shot goal wards which Marriott looked to have covered but allowed it to pass under his body and into the net.
City forced three successive corners in reply, Bell heading the first inswinger away almost off the line.
Stags were forced into a defensive switch on 55 minutes as Martin limped off. Wood came on to play right back, Mullins switched to central defence and Jelleyman to left back.
Stags' lead lasted just 11 minutes as the Imps levelled things up from the spot on the hour.
Buxton was furious when the referee decided he had held Forrester right in front of goal,. But the kick was given and, although Muggleton guessed the right way, the pace of the kick made sure it found its mark.
Seconds after Stallard came on for the Imps Brown was booked for checking Green just outside the box.
With 18 minutes to go, Billy Dearden made a positive double switch, bringing off Brown and Bell and sending on Holmes and debut-making Atkinson.
He almost scored from his first touch as Boulding's flick found Holmes and he shielded the ball before teeing up the Hull youngster for a low shot straight at Marriott.
Nine minutes from time Dawson's ball over the top sent Holmes clear and, as Marriott advanced, he clipped a superb finish past him which came down of the underside of the bar.
The ball stayed loose and Boulding almost got in but hooked wide as Marriott spread himself well.
There was danger for Stags as a Green free kick passed through a crowded box and wide. Brown's header was too high from a corner seconds later and then N'Guessan drilled a low shot wide from distance.
In a thrilling finish Holmes again looked to be going clear on 85 minutes but chose to shoot early and fired straight at the keeper.
Hamshaw tracked back well to stop John-Lewis getting a shot away in the box as we entered three minutes of stoppage time.
And right at the death Stags stole a thoroughly deserved winner, Holmes helping Dawson's ball into the path of Boulding who beat the advancing Marriott and steered it into the empty net to send the travelling fans into wild celebrations.
LINCOLN: Marriott, Green, Beevers, Brown, Ridley, Kerr, Hand, Dodds (N'Guessan 76), Forrester (Smith 82), Wright (Stallard 69), John-Lewis. Subs not used: Hone, Duffy.
STAGS: Muggleton, Martin (Wood 55), Jelleyman, Buxton, Mullins, Brown (Holmes 72), Dawson, D'Laryea, Bell (Atkinson 72), Hamshaw, M. Boulding. Subs not used: Arnold, White.
REFEREE: Phil Dowd of Staffordshire.
ATTENDANCE: 4,280 (734 Stags).
GOALS: Stags - Boulding 49, 90. Lincoln - Forrester 60 (pen).
CAUTIONS: Stags - Brown 69 (foul on Green), Brown 90 (foul on N'Guessan).
MAN OF THE MATCH: Mickey Boulding.
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