The Lions outplayed United from the start and missed a number of gilt-edged chances before finally taking the lead in the 42nd minute through midfielder Jay Simpson, with Neil Harris and Tony Craig both netting in the second half.
The home side should have opened the scoring in the fifth minute when Carlisle keeper Keiren Westwood, fumbled a powerful Harris strike, only to recover well to block at the feet of Bas Savage from three yards.
United defender Peter Murphy nearly turned the ball into his own net in the 10th minute, when he sliced a Simpson cross into the stands.
Savage tried his luck from long range a minute later, but saw his audacious 25-yard effort fly well wide of goal.
Lions midfielder Marc Laird should have done better in the 18th minute when he blasted wide after pouncing on a loose ball on the edge of the box.
Harris missed the target two minutes later, when he clipped the ball inches over the bar after latching on to a clever knockdown from Ahmet Brkovic.
Westwood saved United in the 24th minute when he dived to his left to stop a thunderous strike from Lions skipper Paul Robinson.
The keeper was in action again in the 31st minute, when he dived acrobatically to claw away a curling Harris strike.
The 23-year-old pulled off another magnificent stop a minute later, when he blocked a bullet header from Laird after the defender ghosted into the United box.
The home side were finally rewarded for their efforts in the 42nd minute when Simpson ran on to a clever Harris knockdown and thundered an angled shot past Westwood from 20 yards.
United were reduced to ten men in the 56th minute when skipper Danny Livesey was sent off for scything down Harris inside the box.
The veteran striker picked himself up to double the Lions' lead from the penalty spot.
The home side were rampant and made it three in the 61st minute when Brkovic nodded a deep Harris cross back across goal for Craig to head home at the far post.
United were shell-shocked and the Lions nearly made it four in injury time when Harris saw his powerful 25-yard shot turned around the post by Westwood.