Heatley was joined on the visitors’ scoresheet by Jordan Forsythe and Ben Kennedy in Lurgan - with Glenavon finishing frustrated at two goals disallowed and a penalty appeal dismissed.
Forsythe broke the deadlock with four minutes on the clock.
Heatley came close to kicking off the scoring but for a combination of James Taylor’s save and a Danny Wallace clearance off the loose ball but Crusaders made it 1-0 moments later as Forsythe took advantage of time and space to fire home.
Former Glenavon goalkeeper Jonny Tuffey was alert to collect a long-range Conor McCloskey attempt but the away side enjoyed the upper hand early on.
Forsythe’s angled pass cut open the Glenavon backline and Ross Clarke took a touch but could only slide the ball wide.
An incident involving Paddy Burns heading goalwards with Crusaders’ Billy Joe Burns making the challenge around the edge of the box sparked home appeals but referee Tim Marshall rejected all calls.
Kennedy then scooped over the crossbar from a few yards following good work by Heatley.
However, Glenavon’s second-half response featured early drive and a flurry of talking points within the first 10 minutes after the interval.
McCloskey found Matthew Snoddy in the penalty area with a cross from the right on 46 minutes but the latter’s goal was ruled out for offside.
Andy Waterworth had one shot diverted away by the covering Daniel Larmour as Glenavon pushed forward in search of a way back into the tie.
Waterworth did have the ball in the net on 54 minutes - only for another offside decision to go against the hosts after he tucked home following a scramble in the box, James Singleton deflected shot and save by Tuffey to push the ball towards the Glenavon striker and Wallace unmarked at the far post.
With Glenavon on the frontfoot, Crusaders attempted to take advantage of space behind the backline and the counter-attack plan proved effective before the hour mark.
Heatley displayed a superb first touch to pull down a ball from the back, round Taylor and slot home for 2-0.
On 67 minutes, a measured assist by Forsythe split open the Glenavon defence and Kennedy raced towards the target before curling home a delightful left-foot shot.
Glenavon had a penalty appeal dismissed off a corner-kick before, seconds later, Kennedy slipped in Heatley for number four.
GLENAVON: Taylor, Burns, Haughey, Waterworth, O’Connor, Snoddy, McCloskey, Fitzpatrick, Wallace, Singleton, Ward.
Subs: Stafford, A.Doyle, Hall, Beggs, Scannell, Hunter, J.Doyle.
CRUSADERS: Tuffey, Burns, Wilson, Weir, Lowry, Kennedy, Forsythe, Larmour, Heatley, Robinson, Clarke.
Subs: O’Neill, Hegarty, Lecky, Frazer, Caddell, O’Rourke, Owens.
referee: Tim Marshall.
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