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The Crues lead Linfield, who lost 1-0 at Glenavon, by nine points, with just five sets of fixtures remaining.
Neil McCafferty gave the Bannsiders the lead with a penalty but goals from Billy Joe Burns and Jordan Owens (2) put the Crues in control at half-time.
Paul Heatley scored twice after the break and Michael Doherty was sent-off.
Crusaders could effectively win the Premiership by beating Linfield at Windsor Park next Saturday as that would extend their lead at the top to 12 points, with a much superior goal difference.
Doherty produced a fine save from Heatley in the opening minute, while the home keeper made another impressive stop from a Colin Coates drive.
The Bannsiders took the lead on 20 minutes when McCafferty rolled the ball into the corner of the net from the spot after Darren McCauley had been tripped by Josh Robinson, his 12th league goal of the season.
Burns replied two minutes later by drilling a low free-kick into the net and the full-back turned provider in the 28th minute, crossing the ball for Owens to head home unmarked from six yards out.
Owens grabbed his second when he swivelled and fired into the bottom corner from inside the box four minutes later.
A minute after the interval, Heatley rifled in a left-foot shot across Doherty, who should have done better.
The livewire winger added another soon after with a glancing back-post header into the bottom corner.
Crusaders manager Stephen Baxter: "We were magnificent today - we blew Coleraine out of the water after going behind.
"We played really well. If you play the right balls to the right players in the right positions, then you are going to score goals.
"There were a few harsh words said at half-time, we scored two goals soon after the break and that was the game over.
"We're not getting carried away though. We will just prepare in the normal fashion and get ready for a huge game next Saturday."
Crusaders took a massive step towards winning the Irish League title for the first time in 18 years by hammering 10-man Coleraine at Ballycastle Road.