Chances were few and far between in the opening 25 minutes with Peter Campbell's delivery easily gathered by Declan Dunne and Matthew Snoddy unable to keep his strike from range on target for Paddy McLaughlin's side.
Dungannon's best chance early on came when Leo Alves fired a loose ball towards goal, but Mark Byrne was able to thwart the chance at the near post.
Glenavon opened the scoring just before the half hour after Chris Atherton's corner was recycled back to the 16-year-old with his second delivery nodded towards goal by Snoddy, forcing Dunne to make a good save to tip the danger away.
Snoddy was able to get to the rebound, but once again his shot was deflected. However, Davy McDaid was able to nod home from close range for his third goal in three games.
McDaid was then denied a second goal by the inside of the left-hand post after he had been played through on goal by Len O'Sullivan and tried his luck from a tight angle. Campbell latched onto the rebound but couldn't get a shot away.
The striker was involved in Glenavon's second goal though as his pass, which deflected off the torso of Gael Bigirimana, was met by a superb first-time finish from Malone, which flew into the top corner.
It was the perfect start to the second half for the Tyrone club as they were awarded a penalty just 60 seconds after the restart when McGovern fell under the challenge of Barney McKeown, with McGovern stepping up and making no mistake with the resulting spot-kick.
Both sides then had good chances with Malone and Adam Glenny both firing narrowly wide.
The equaliser came in the 65th minute with substitute Mitchell heading a well-timed cross from Scott past Glenavon stopper Byrne.
The tempo of the game then dropped but the goals weren't with Malone netting his second of the evening and putting Glenavon ahead once again after Malone finished after the ball was played back to him by substitute Paul McGovern.
Dungannon pushed for another goal until the final whistle with Tomas Galvin being denied by a superb diving save by Byrne before Rhys Marshall cleared Andrew Mitchell's shot to safety.