At the Showgrounds, Coleraine should have been ahead inside the opening few minutes but Matthew Shevlin passed up a golden chance to score his 13th of the season.
Cooper did brilliantly to beat his man on the wing before delivering a cross to the back post onto the head of his strike partner.
With the goal at his mercy Shevlin rattled his header off the crossbar and the chance was gone.
Linfield responded and Matthew Fitzpatrick was guilty of missing their best chance following a Coleraine defensive mistake, but he blasted wide of the target when well positioned.
At the other end Chris Johns produced a fine diving save to deny Lewis McGregor just before half-time.
The deadlock was finally broken seven minutes after the restart thanks to one-time Linfield favourite Cooper.
Shevlin did well to get a flick on to a Lyndon Kane punt forward and Cooper did the rest, racing clear of the Linfield defence to plant a left foot shot wide of Johns and into the far corner of the net.
The lead should have been doubled just minutes later when Dean Jarvis picked out Shevlin with a pinpoint cross but Johns produced a fine save at his near post.
But home fans didn’t have to wait too long as second half substitute McGonigle scored within moments of replacing Cooper.
Again, Shevlin provided the assist, flicking on a goalkeeper’s clearance into the path of the Dungiven man who took a touch before rifling the ball into the bottom corner of the goal.
Linfield were thrown a lifeline in added time when Dean Jarvis handled inside the penalty area and McKee calmly slotted home from 12 yards.
But the final word went to the home side as Patching curled home a delightful effort from the edge of the penalty area to make the points safe and condemn their opponents to three league defeats in a row for the first time in eight years.
