Hallam Hope's first-half header gave nine-man Carlisle a 1-0 win and sent Crawley spinning to a fifth defeat in six home league games.
Reggie Lambe was an unused substitute.
Both teams had players sent off in stoppage time as the match ended on a bad tempered note.
Carlisle had the ball in the net in the 15th minute but Hope's close-range effort was ruled offside following a move involving Nicky Adams and Shaun Miller.
Crawley threatened midway through the half when a cross by Dutch winger Enzio Boldewijn set up Jordan Roberts and his low shot was saved by the legs of goalkeeper Jack Bonham.
Bonham, recalled in place of Shamal George, came to Carlisle's rescue again by blocking a goal-bound volley from skipper Jimmy Smith from Boldewijn's cross.
Crawley have only won twice at home in the league since mid-January and were dealt a blow six minutes after the interval when Hope broke the deadlock with his third goal of the season.
Hope, recalled in place of Lambe, was given time and space to head in a deep cross from former Crawley winger Adams.
Carlisle were reduced to 10 men with 15 minutes remaining when substitute Richie Bennett was shown a straight red card for elbowing Crawley defender Josh Yorwerth.
Carlisle also had Tom Parkes dismissed in time added on following a flare-up inside the Carlisle penalty area which also saw Yorwerth sent off.
Crawley's Lewis Young and Boldewijn were also booked as a result of the incident.