Linfield captain Jamie Mulgrew said in the build-up to the game that he hoped that winning the Irish Cup would soften the blow of losing out on the Irish Premiership title to Larne, and the Blues certainly started like a side out to prove a point.
Chris McKee and Joe Cooper forced David Odumosu into two early stops at a sold-out Windsor Park, which was a cacophony of noise.
They then deservedly made the breakthrough on 14 minutes as McGee darted in front of Shea Kearney and rose highest to head home from Kirk Millar's inviting free-kick from the right-hand side.
That was the first goal Cliftonville had conceded in this year's competition, and they seemed shell-shocked by it as they struggled to impose themselves on the game.
It continued to be one way traffic for Jim Magilton's side with Kyle McClean then testing Odumosu.
The Reds fashioned their first chance of the game on 25 minutes with their first real passage of play.
Sean Stewart fed Rory Hale, whose deep cross was inches away from finding Ashford at the back post.
Ronan Doherty then curled an effort well wide after another promising move.
Cliftonville's afternoon went from bad to worse however, when first-choice goalkeeper David Odumosu and centre back Odhran Casey both forced off with injuries before half-time.
