Ronan Mclaughlin fired the home side ahead in the 7th minute despatching a twenty yards free low to the corner past Ben Miller.
The colts replied and Cory O’Brien raced clean through but was denied by Declan Caldwell in the home goal before Shane Meehan should have done better than head wide when unmarked.
Cockhill blitzed the visitors with three goals in nine minutes courtesy of a Shane A Doherty hat trick.
Firstly he got on the end of a david laird cross to slot home from close range before repeating the feat from a Marty Doherty crossfield ball.
Then on 42 minutes he collected a pass from laird and made space before curling a superb effort to the top corner to leave it four nil at the break.
Six minutes after the restart they made it five when jack Mcdaid surged into the area before firing to the net from a tight angle.
Gleneely to their credit battled hard and got a goal back when Billy Mccann crossed for Meehan to hammer home from ten yards.
But Cockhill substitute Shay Mclaughlin made it six one when Daniel Martin Doherty unselfishly set him up to slot home from close range.
Another substitute Michael Owen Doherty added a seventh with a superb lob from the edge of the area.
The colts got a consolation in the final minute when Dylan McDaid converted a penalty after McCann had been tugged back.