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Reds midfielder Ryan Catney sustained a broken leg and was shown a red card following a first-half tackle before Michael Carvill scored for the Crues.
Mark Stafford and Andrew Waterworth netted for Linfield while Glenavon beat Portadown 2-1 in the mid-Ulster derby.
Coleraine defeated Ballinamallard 2-1 and Dungannon won 1-0 at Carrick.
Crusaders had to work hard for their home victory over their north Belfast rivals.
"It was a great through ball by Jordan Forsyth, I found myself in the box and was happy to see it in the back of the net," said match winner Carvill.
The Crues have lost just two of their 26 league matches this season and are well on course for a third successive Gibson Cup success.
Linfield kept up the pressure, though, by beating Ballymena at Windsor Park.
Defender Stafford's shot went in off a defender for the opener in the first half with striker Waterworth securing the victory with a late second.
Ballymena's defeat meant Coleraine took over in fourth place by winning 2-1 away to Ballinamallard United, Jamie McGonigle scoring both of their goals at Ferney Park.
Premiership leaders Crusaders beat 10-man Cliftonville 1-0 to stay seven points ahead of title challengers Linfield who beat Ballymena United 2-0.