Just three minutes into the game, the Larne support were up on their feet when Ryan found the back of the net, but the flag had been raised as the Scottish striker was offside.
Larne continued to enjoy more possession as Kealan Dillon made a late clearance off the line to keep out Matt Ridley's header.
The Inver Reds' persistence paid off, and they opened the scoring after just 12 minutes when Ryan nodded home a well-timed delivery from Jordan McEneff on the right wing.
Ryan nearly doubled Larne's lead minutes later, but Dylan Glass made himself big and blocked the shot before making a similar save to deny Lusty's effort shortly after.
However, that didn't deter the Larne players, nor fans, and the side kept pushing for a more comfortable lead.
Larne doubled their advantage on 21 minutes when Caolan Marron was caught sleeping in Dungannon's defence and Leroy Millar was able to win back possession and feed the ball for Lusty to convert.
Another mistake from the away side gifted Lusty another chance and the striker charged forward and slotted home to extend their lead.
Another great save from teenager Glass denied Lusty a first-half hat-trick after he rushed off his line to deflect his effort.
As the half-time whistle approached, Ryan fired just wide before his delivery was just too heavy for Sean Graham.
Lusty completed his hat-trick just two minutes after the restart when his left-footed effort from the edge of the box found the bottom corner.
The goals kept coming as McEneff's low corner from the edge of the box found the unmarked Ryan, who converted for his second and Larne's fifth in the 53rd minute.
Sean Graham charged forward and added a sixth after he latched onto a long ball, weaved his way around Peter Maguire and found the back of the net.
Ryan then joined fellow Larne striker and secured a share of the match ball when Paul O'Neill unselfishly squared the ball to Ryan to fire home on 72 minutes.
Substitute O'Neill would score himself with just 11 minutes to go with a lovely looping strike from range.
Despite the Swifts, who will defend their Irish Cup title next Saturday, having a few half chances as the full-time whistle approached, they couldn't find a way past Rohan Ferguson who claimed his 21st clean sheet of the season.
At the full-time whistle, Inver Park erupted as the home fans made their appreciation known for their side, who guaranteed there would be no final day twist and turns in the Irish Premiership.