United could have opened the scoring with just 50 seconds on the clock when a ball over the top fell nicely for Asamoah. He caught it on the run but his attempted lob dropped just over the angle of post and bar.
The home side took the lead as they built on a positive start to the game when a direct run through the heart of the defence was finished off with a crunching shot into the bottom corner.
The Blues then started to take control and they were back on terms midway through the half when Louis Pedro, set to sign a short-term contract this week, stepped in to poke the ball over the line following a goal mouth scramble from a dangerous Smith cross.
Visiting chances started to flow and Balanta was a whisker away when he glanced a dipping cross from McQueen just wide of the mark.
The impressive Patrick Brough found joy on the left flank, as he linked well with Gillesphey, and Asamoah went close when he volleyed one of a succession of telling crosses past the post from the edge of the box.
Carlisle picked up the tempo and they took the lead through a stunning strike when Hery latched onto a loose ball in midfield. He carried it forward and left the keeper with no chance as he put his boot through an unstoppable shot.
The lead was extended on 67 minutes when Hery curled a corner into the box. Rigg flicked it on and Archibald-Henville did the rest as he guided a bullet of a volley into the top corner.
And Louis Pedro made it four goals in two games with a fine individual effort with ten minutes left to play. He twisted and turned with his back to goal and unleashed a 20-yard curler as he spun his man and found the back of the net via the inside of the upright.
United - Hanford (Williams 73), McQueen, Archibald-Henville, Gillesphey, Brough, Pedro, Smith (Thompson 46), Sweeney (Pearson 46), Hery, Balanta (Thompson 46), Asamoah (Rigg 46).
Goals - Pedro (23 & 81), Hery (31), Archibald-Henville (67)
Booking - Smith (14)