Guy Bates scored twice as the Lurgan Blues secured a first Premiership win since mid-December, halting a dismal six-game losing run.
But that tells only part of the story of a dramatic and at times ill-tempered Mid-Ulster derby.
A chaotic match saw Glenavon recover from a goal and a man down as Dungannon’s hopes of stretching their unbeaten Premiership run imploded.
How Swifts managed to throw this game away from such a good position will leave Darren Murphy bewildered and frustrated in equal measure.
They seemed on course for another vital win when James Costello scored his first goal for the club, minutes before Niall Henderson was sent off.
But Bates soon levelled from the penalty spot, signalling the start of a dramatic turnaround.
Dungannon themselves were reduced to 10 men in the second half when Emmet Friars was red-carded for a professional foul.
Mark Farren then put Glenavon in front before Bates’ late, late strike secured the win.
Although bitterly disappointing for Dungannon, they can have few complaints with the result.
The home side showed a greater drive and determination, particularly in the second half, albeit they benefited from some shocking defending.
With Glenavon climbing above Swifts in the table, it is a gentle reminder that Premiership survival is not yet secured.
Dungannon had won the sides’ previous two meetings this season, and were on course to make it three when they raced into a 21st minute lead.
Ryan Harpur was the architect and Costello’s header went in via the underside of the crossbar.
The home side’s chances suffered a further hit when they were reduced to 10 men.
Henderson appeared to swing an elbow at Matt Hazley, resulting in a red card. He also clashed with Harpur, unhappy with his role in drawing the referee to the incident.
Suddenly Glenavon were faced with a similar situation to the last meeting here in late August, when they played an hour with 10 men.
But unlike that game, when Dungannon held on for a 1-0 win, the home side were soon level.
Jonny Curran was penalised for bringing down Farren in the area, and Bates crashed home the resulting penalty with a powerful strike.
Dungannon almost retook the lead late in the half. Chris Lavery was played through on goal, but his low drive drew an impressive stop from Andy Coleman.
Glenavon started the second half strongly and had a massive penalty shout when Farren seemed to be taken down in the box by Curran.
However, referee Mervyn Smyth rejected their appeals – and booked the striker for diving.
It was a big call, but Dungannon’s luck did not hold.
Two minutes later Friars was red-carded for pulling back Bates outside the box and, to make matters worse, it led to a second Glenavon goal.
The free-kick was fired into the wall, but Gary Hamilton switched it to Farren at the back post and he converted with a side-foot finish.
Costello nearly levelled again with a snapshot before a Glenavon counter-attack ended with Kyle Neill’s strike being deflected just off target.
The game was now end-to-end, with Harpur’s cross-shot being tipped over by Coleman.
Yet Glenavon always looked the more likely to score on the break and they secured the points four minutes from the end.
A long ball from Mark Haughey caught out the visitors’ defence and Bates rounded the ‘keeper before hammering home their third.
GLENAVON: Coleman, Neill, McCallion, Haughey, Kilmartin, Bates, Farren (Rooney, 79), Brown, Henderson, Hamilton (McGrory, 72), Gardiner (Doherty, 57)
Subs not used: Dane, McDaid
DGN SWIFTS: Curran, O’Neill, Montgomery, Friars, Grieve, McKerr, Harpur, Hutchinson, C Lavery (PJ Lavery, 64), Hazley (Topley, 59), Costello (Cahoon, 75)
Subs not used: McMinn, Brennan
Referee: Mervyn Smyth (Belfast)