It was more of the same from the Crues after the break and they won a free kick 10 yards inside the Glentoran half.
Levadia's superior fitness told in the latter stages and Crues survived a major scare on 75 minutes when the ball fell for Rakhmanov inside the area, only for the Bulgarian's shot to ricochet off a defender and strike a thankful O'Neill.
BRU UP: Crues players celebrate League Cup win BRUCEY BONUS: Colin Morrow celebrates Crues winner
The Crues boast a terrific recent record against the Glens, winning nine of their last 13 league meetings.
Cockcroft, 20, who spent part of last season with Ards, is determined to repay Crues boss Stephen Baxter's faith in his ability as a free running wideman.
Morrow forced Alan Blayney into a flying save as the Crues took an early hold on the game, but they were unable to make their superiority pay.
The Reds hold a one point lead over Linfield, who defeated nine-man Crues 3-2 on Saturday, heading into the last three games of the campaign.
The Crues made light work of the basement side, coming back from an early Ross Arthurs goal to complete a comprehensive win with goals from Gary McCutcehon, Jordan Owens and Eamon McAllister (two).
The Crues were celebrating this time after goals from man of the match David McMaster, a John Convery own-goal and Jordan Owens gave Stephen Baxter's troops a four-point lead at the top of the Carling Premiership table last night.
Warr'point 1 Crues 1 CRUSADERS were left to rue missed chances as they lost ground in the title race at Milltown on Saturday.
CRUES boss Stephen Baxter laid the blame firmly at the feet of referee Adrian McCourt after this furious Boxing Day fiasco.
Matthew Snoddy gave the Crues an early lead from the spot, before Stephen Brown - who was later sent off for a second yellow card - levelled after the break.