It was a disappointing start for the Millers, who looked off the pace in the first half in particular. They improved in the second period and after Tyler Blake equalised they had opportunities to secure the win, but overall they could have no complaints about the result.
Managers Tommy Brookbanks and Mark Harvey went into the game without Dan Brown and Daniel Fletcher (suspended) and Aaron Opoku (injured). That meant an intended start for Daryll Thomas but he injured himself in the warm-up and so that led to a full debut for Jordan Smith.
In front of an impressive crowd of 190 it was the Whites who started the sharper and Kalum Smith fired an early effort across the face of goal.
Carlton responded and when Oliver Clark was brought down on the edge of the box Tom Maddison fired a free kick over the bar.
Lawrence Gorman went down under a heavy challenge from Jake Park and eventually had to be substituted but by then Lincoln were ahead. There seemed little danger when they advanced down the right but Rob Smith found himself with space in the area and he fired low into the corner of the net.
Carlton had to make another enforced change before half time when captain Maddison went off injured as Lincoln ended the half on top.
The Millers were much improved in the second half and Tyler Blake equalised on 53 minutes. A free kick was delivered into the area, Clark headed onto Jordan Smith whose clever pass set up Blake to slot home.
Five minutes later Carlton were desperately close to taking the lead. A fierce Clark drive was excellently palmed away by Michael Antkowiak. Jordan Smith did well to keep the ball in play and he played another lovely ball across the face of goal with Blake inches away from tapping in.
Eli Bako then did well before feeding Martin Ball. Ball hit a deep delivery to Blake who had stolen away from his marker. With the goalkeeper off his line Blake lofted a header just over the bar.
It was a key moment as Lincoln went up the pitch minutes later and regained the lead. Matthew Cotton slipped the ball to Jack Mcmenery who took a touch and then fired into the top corner from 20 yards.
Carlton almost levelled again when Clark headed just over after Toby Moore had headed a Niall Davie corner back across goal and Lincoln were reduced to 10 men on 81 minutes when Sidhei Costa was shown a straight red card for a poor tackle on substitute Patrick Quinn.
With time running out another Davie free kick led to a scramble in the area where any kind of touch would have led to a goal but Antkowiak was able to save.
With the game in the fifth minute of added time Lincoln sealed the win. A free kick from Dave was cleared, Lincoln broke at pace, Rob Smith beat Steggles to the ball and tapped into an empty net.
The result left plenty for the Carlton managers to ponder ahead of a difficult away trip to Banbury Utd on Tuesday in the FA Cup.
Carlton Town: Steggles, Gorman (Sturgess 38), Johal, Ball, Moore, Maddison (Bako 42), Elliott (Quinn 77), Clark, J Smith, Blake, Davie. Unused substitutes: Randall, K Wilson
Goals: Blake 53; Rob Smith 28, 90, Jack Mcmenery 75
Carlton Town Supporters Club MOTM – Oliver Clark