Coleraine recovered from their three-match losing streak by beating the Reds, who drop to third in the table.
The Bannsiders had won the last two league matches between the sides and Shane McGinty put the hosts ahead with a left-foot finish off the post on 43.
Howard Beverland added the second with a diving header from Neil McCafferty's corner midway through the second half.
Michael Doherty made fine saves from Joe Gormley and Barry Johnston while Jay Donnelly hit the bar with a header.
The home side had the better of the first half and Darren McCauley forced a fine save from Conor Devlin, before providing the back-heel for McGinty's opener two minutes before the interval.
Doherty made a fine stop from David McDaid's flick and Gormley's thundering right-foot shot, before Beverland nodded in from close range to extend his side's advantage.
Doherty saved low to his right from Johnston, the impressive McCauley fired over the bar and then Donnelly went close with that late chance.
Cliftonville now trail leaders Portadown by three points and second-placed Linfield by two.
Coleraine manager Oran Kearney: "We had a good spell of pressure in the first half and it was important that we capitalised on that, so the goal before the break was very important.
"Our mentality was important today, even more than our tactics, I'm delighted with the way the players went about their business."
Cliftonville manager Tommy Breslin: "We were particularly poor in the first half - we looked lethargic and tired, but we were better in the second half and created some chances.
"It was just one of those days - we're disappointed but we'll move on, it's only one game."