Glenavon produced the better start with both King and Neill testing Bannsiders keeper O'Hare early on.
Shell-shocked Glenavon staged a revival with Trevor Molloy completing his hat-trick and James Costello making it 5-4.
Glenavon's penalty was also for hand-ball, Andrew Kilmartin the guilty party this time from Sammy Stewart's cross.
Former Northern Ireland international and Glenavon favourite McBride became part of Cochrane's management team during the Spring.
Glenavon said that they hoped to confirm the new management structure before the end of this week.
The win moves Glenavon up to second place in the table - one point behind leaders Glentoran.
The Reds striker topped the poll ahead of second-placed Jimmy Callacher of Glentoran and Glenavon's Mark Haughey.
Crusaders had a chance to equalise on the half-hour but Glenavon goalkeeper Tuda Murphy blocked Rainey's pointblank effort.
Ballymena United scored twice in the dying seconds to claim a 3-3 draw with Glenavon at the Showgrounds.
Trevor Molloy scored two early goals, one a penalty, for Glenavon but Jordan Owens netted twice for the Crues.
Grant headed Glenavon into the lead on 50 minutes as he powered a Stuart King cross past Sean O'Neill.
Miskimmin made his competitive debut for Glenavon after his recent move from Linfield.
Glenavon go into the game second on goal difference in the table after opening wins over Coleraine and Portadown.
Albert Watson held talks with Glenavon boss Marty Quinn in January and could move from the Showgrounds to Mourneview Park.
Crusaders held on for the win which lifts them above Glenavon, Linfield and Cliftonville and into third place in the table.
Spence's penalty was a massive blow to Glenavon who looked set to go into the interval a goal to the good.
Tony Grant looked to have earned Glenavon a point as he headed home on 77 but Caldwell lobbed the late winner.
Fraser was in charge of Glenavon in the early 1990s and also was part of the staff of previous manager Colin Malone.
Cochrane's Glenavon had been beaten 2-0 by champions Linfield the previous weekend.
Glenavon broke the deadlock when Molloy was left unmarked at the back post to head in James Costello's cross past Gavin Cullen.
Stuart King and Kyle Neill both tested Davy O'Hare early on before Miskimmin headed Glenavon into the lead after a James Costello cross.
Glenavon's Trevor Molloy then saw a penalty well saved by Whites keeper Philip Matthews and Gary Liggett put Distillery two in the 54th minute.
The Glenavon statement said that the club's board of directors thanked "Terry Cochrane for his services and wishes him well in his future career".
Eamon Murray put Glenavon ahead at Seaview with a third-minute goal but Barry Spence levelled on the stroke of half-time from the penalty spot.
Glenavon keeper Andy Plummer made a double save to deny David Scullion and Gareth Harkin before Miskimmin scored his second after an O'Hare mistake.
Distillery's second came when a long ball caught out McDonagh and former Glenavon striker Liggett took advantage to slide his shot under keeper Andrew Plummer.
Miskimmin missed a further second-half chance but Glenavon had done enough.
Gary McCutcheon put United in front but Gary Hamilton (2) and Kyle Neill gave Glenavon a 3-1 lead before late strikes from Albert Watson and McCutcheon.
However, Glenavon restored their lead within two minutes as Grant powered a close-range header past O'Neill after the Swifts keeper had only been able to parry a Molloy pile-driver.
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