A 50th minute goal by Hallam Hope settled the game as Crawley left the field to boos from the home crowd.
Harry Kewell made two changes to the side which lost to Newport County in midweek.
Danny Bulman and Josh Payne came into the side in place of Ibrahim Meite and Aryan Takbahsh who were on the bench.
Reds played three at the back when in possession with Josh Yorwerth, Mark Connolly and Josh Lelan as centre-backs.
When attacking, Lewis Young and Cedric Evina moved forward as wing-backs, while Jimmy Smith formed a front-three with Boldewijn and Roberts in a 3-4-3 formation.
When Carlsile had the ball it switched to 4-4-2 with Smith back in an advanced midfield role and either Evina or Young joining the back-four.
Carlisle were first out of the blocks and in the 15th minute had a goal disallowed for offside when former Crawley players Shaun Miller and Nicky Adams put Hallam Hope through for a tap-in.
Reds carved out their first chance on 22 minutes when Enzio Boldewijn crossed to Jordan Roberts who shot low but the ball was saved by keeper Jack Bonham’s legs.
Then Enzio crossed for Smith to shoot but again he was denied by good work from Bonham.
Carlisle took the lead early in the second half when Adams crossed to Hope who headed home.
The visitors nearly made it 2-0 on the hour as Luke Joyce blazed an angled shot over the bar.
Kewell brought on striker Ibrahim Meite in place of Lelan and at times played four up front as they went in search of an equaliser.
Carlisle were reduced to ten men on the 74th minute when substitute Richie Bennett elbowed Yorwerth.
Kewell responded by bringing on the pacey Panutche Camara for Evina.
In the final stages Boldewijn tried to find Smith at the far post for a header but the pass was too long and he was off-balance as he headed over the bar.
However despite plenty of good passing in patches, Reds failed to really threaten to score in the whole of the second half.
A fight broke out in the Carlisle penalty area druing added-time resulting in straight red cards for Yorwerth and United’s Tom Parkes plus yellow cards for Young and Boldewijn.
This means Carlisle had to finish the game with only nine men while Crawley had ten.
REDS: Morris, Young, Payne, Connolly, Boldewijn, Smith (capt), Roberts, Yorwerth, Evina (Camara 78), Bulman, Lelan (Meite 61)
Unused subs: Doherty, Mersin, Tajbakhsh, Randall Sanoh
CARLISLE: Bonham, Grainger (capt), Joyce, Parkes, Jones, Hope, Adams (Devitt 71), Brown, S.Miller (Bennett 61), Etuhu (Liddle 90, Hill
Unused subs: T.Miller, Cosgrove, Lambe, George
REFEREE: Kevin Johnson
ATTENDANCE: 2,021 (358)