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Rodney Brown nodded in from a Brad Lyons cross to put the Bannsiders ahead but the Blues hit back with Aaron Burns heading home the equaliser.
Matthew Clarke's side-foot finish moved Linfield in front before Coleraine defender David Ogilby was sent-off for two yellows on 67 minutes.
Jamie Mulgrew poked in Linfield's third as they maintained their 100% record.
Coleraine made the early running and were rewarded on 23 minutes when Brown scored against his former club with a downward header into the bottom corner.
Blues forward Guy Bates had almost sent a clearance into his own net and headed wide of the Coleraine goal before he set up Linfield's two first-half goals.
His dinked cross picked out the unmarked Burns as the midfielder netted his fifth goal of the campaign while Clarke rifled home from a tight angle at the back post.
Lyons saw his goalbound shot deflected over by Sean Ward before Clarke's goal while Brown went close twice before the break.
A dull second half came to life when Ogilby was controversially dismissed after the defender appeared to make minimal contact with Andrew Waterworth.
Linfield capitalised with the extra man two minutes later - substitute Mulgrew jinked into the box before prodding the ball beyond keeper Michael Doherty.
"We knew it was going to difficult and this was about the result, not the performance," said Linfield boss Warren Feeney.
"We started slowly but showed tremendous character to come from behind to win."

Mr Piech had criticised his chief executive in an interview with the German news magazine Der Spiegel, but did not specify the issue at stake.
Mr Winterkorn has been widely tipped as VW's next chairman. Mr Piech and the Porsche family control 51% of VW.
Volkswagen is the biggest car manufacturer in Europe.
On 17 April, Volkswagen's five-member governing board gave its backing to Mr Winterkorn.
Board member Wolfgang Porsche, a cousin of Mr Piech, said he had given his "personal opinion" without clearing his remarks with other family members.
Mr Piech, 78, is a former VW chief executive. His wife Ursula has also resigned her seat on the board.
In a statement (in German), Volkswagen said that deputy board chairman Berthold Huber would serve as interim chairman.
During his eight-year tenure as chief executive, Mr Winterkorn has overhauled VW and made it one of the world's most successful carmakers, industry analysts say.
In 2014, VW was the world's second-biggest carmaker by sales, behind Toyota and ahead of GM.
Apart from Volkswagen, the group's brands include Audi, Porsche, Lamborghini, Bugatti, Bentley, Skoda and Seat.

Root, 25, made his Notts debut in 2016 and his breakthrough came this season when he made 107 from 93 balls against Warwickshire in the One-Day Cup.
Bowler Luke Fletcher has also signed a new two-year deal at Trent Bridge.
Fletcher, 28, was struck on the head while bowling at Edgbaston in July - an injury that ended his season.
Before the incident, he took 36 wickets at 22.44 to help Notts move clear at the top of County Championship Division Two.
"It's a well-deserved contract for Luke because of what he has done in the last 12 months," said Notts head coach Peter Moores.
"He's gone away and looked quite hard at what he can do to get himself into the team.
"We have seen the results of that in the way he bowled in the first part of the County Championship."
Root came through the Yorkshire Academy before being released in 2011 and joining the MCC Young Cricketers.
He is now a regular in white-ball cricket for Notts and Moores wants him to push for a place in the four-day team.
"He's been an effective player for us, particularly in one-day cricket," Moores continued.
"We're looking for him to now push on in both white and red-ball cricket after working very hard for this opportunity."
Linfield remain top of the Irish Premiership after overcoming 10-man Coleraine at the Showgrounds.
[NEXT_CONCEPT]
The chairman of the carmaker Volkswagen (VW), Ferdinand Piech, has resigned after a power struggle with chief executive Martin Winterkorn.
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Billy Root, the younger brother of England captain Joe, has signed his first professional contract, agreeing a two-year deal with Nottinghamshire.