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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."
Linfield remain top of the Irish Premiership after overcoming 10-man Coleraine at the Showgrounds.