Linfield opened the scoring after a quarter of an hour thanks to Fitzpatrick's third goal of the campaign.
Much of the credit, though, goes to assist king Kirk Millar whose in-swinging free-kick was begging to be headed.
And headed it was by Fitzpatrick, who timed his run perfectly to guide the ball low past Aidan Harris and into the bottom corner of the net.
Millar almost added a second when he struck the woodwork after his corner had been cleared back to him and went close again moments later after Coleraine struggled to deal with an Ethan McGee long throw, with Millar's volley going just the wrong side of the crossbar.
A second goal duly arrived, eight minutes before half-time, and again Millar was involved.
His corner caused panic in the Coleraine defence, allowing an unmarked Roscoe to arrive late at the back post to tap into an unguarded net.
Coleraine created very little in the opening 45 minutes, their one bright moment coming when it was 1-0 as Shevlin headed Zane Okoro's clever cross straight into the arms of Linfield keeper Chris Johns.
Shevlin wasn't to be denied after the restart as he hauled the hosts back into the game 10 minutes into the second half.
Substitute Lewis McGregor did brilliantly, getting to the byeline before crossing low into the penalty area, and there was Shevlin to score at the second attempt to bring up his century of goals for the club.
Fitzpatrick passed up a great chance to put the game to bed when he blazed over the crossbar and Linfield were made to pay when the Bannsiders levelled eight minutes from time.
Will Patching delivered a corner to the back post where, after a spot of pinball, Dunne reacted quickest to poke home his first goal for the club.
Both sides passed up chances to win the game and were forced to settle for a share of the points after a thrilling match in front of a sold-out Showgrounds.