The Reds weathered an early storm by the hosts and grabbed the opener on the stroke of half time when Joe Gormley found the net with a close-range header after Liam Boyce's effort had been partially cleared.
Boyce got himself on the scoresheet early in the second half, and Stephen Garrett netted the third after a goalmouth scramble.
Paul Owens did his best to pull the Bannsiders back into the contest with a goal in the 75th minute, but his effort was cancelled out in spectacular fashion by a long-range strike from Barry Johnston five minutes later.
Johnston pounced on a poor clearance from Coleraine stopper Michael Doherty and unleashed a shot from close to the halfway line which sailed over the stopper's head and into the goal.
A late strike from Diarmuid O'Carroll wrapped up a memorable win for Tommy Breslin's side which ended a run of 14 games without a win over Coleraine, and saw them move to the league summit on goal difference.
At the Oval, meanwhile, it was honours even between Glentoran and Linfield in the first Big Two meeting of the season.
Billy Joe Burns denied Glentoran yet another victory over Linfield as his equaliser secured a point for the champions.
The Glens beat their fierce rivals on all four occasions in the league last season, but the Blues got the monkey off their back thanks to a goal on the hour mark.
Andy Waterworth scored his third goal in four games to put the Glens in front but Burns' hit back to earn a deserved draw in a reasonably entertaining Big Two clash.
The game was only seven minutes old when Jim O'Hanlon's superb cross was converted by Waterworth after the striker had nipped in ahead of William Murphy to shoot past Alan Blayney.
Elliott Morris tipped away a Brian McCaul effort on 13 minutes then on 21 minutes it was former Linfield defender Marcus Kane who came to the rescue for Glentoran as his brilliant tackle denied Robert Garrett who was bearing down on goal.
Jim O'Hanlon fired just wide for the Glens on 33 minutes and just after the break Calum Birney's strike from a John McGuigan pass was deflected wide by William Murphy.
Jimmy Callacher and Andy Waterworth had further opportunities before Linfield began to stamp their authority on the game having made a change at half time with Mark McAllister coming into the fray in favour of Mark Carvill.
On 60 minutes McAllister played in Burns who cut inside and fired into the top corner from 16 yards.
Peter Thompson lobbed the onrushing Elliott Morris, but failed to find the net on 73 minutes and Burns shot just wide two minutes later.
Then in the final minute Ryan Henderson should have won it for the Blues when he got on the end of a McAllister cross but headed just wide under pressure from Jay Magee.
In Saturday's other game Ballinamallard United suffered their first defeat of the season as they went down 2-1 away to Crusaders.
The Mallards started brightly and went in front after 21 minutes when Mark Stafford forced the ball in from a Chris Curran corner.
However, Crusaders were back on terms ten minutes before the break when Timmy Adamson's deft touch carried the ball past Alvin Rouse and into the net.
Adamson doubled his tally four minutes after the restart with a fine header from a Gary McCutcheon cross to seal a valuable win for Stephen Baxter's side.
On Friday night, Ballymena United beat Lisburn Distillery 2-0 at the Showgrounds.
An own goal from Jonathan Harkness went in on the stroke of half time, before Neil Lowry scored on 88 minutes to secure victory for the home side.
Elsewhere, Donegal Celtic and Glenavon shared the points with a 1-1 draw at Suffolk Road.
Guy Bates put the Lurgan club in front on 74 after Mark Haughey was sent off for a foul on Mark Miskimmin - Miskimmin later got the equaliser with an 84th minute header.
Dungannon Swifts and Portadown also drew 1-1, with Joshua Cahoon and Darren Murray the scorers.
Saturday's results in full:
Coleraine 1-5 Cliftonville
Coleraine: Paul Owens 75.
Cliftonville: Joe Gormley 45, Liam Boyce 54, Stephen Garrett 60, Barry Johnston 83, Diarmuid O'Carroll 90.
Crusaders 2-1 Ballinamallard United
Crusaders: Timmy Adamson 35, 50.
Ballinamallard: Mark Stafford 21.
Glentoran 1-1 Linfield
Glentoran: Andrew Waterworth 7.
Linfield: Billy Joe Burns 61.
Friday's results in full:
Ballymena Utd 2-0 Lisburn Distillery
Ballymena Utd: Harkness 45 (OG), Lowry 88.
Donegal Celtic 1-1 Glenavon
Donegal Celtic: Miskimmin 84.
Glenavon: Bates 74.
Dungannon Swifts 1-1 Portadown
Dungannon Swifts: Cahoon 90+2.
Portadown: Murray 80.