The 20-year-old claimed frames one and two before Shoot-Out champion Hawkins levelled, racking up a break of 78 along the way before scoring 68 to tie the match once again at 3-3 after Lisowski had re-taken the lead.
That set up a cracking seventh and deciding frame, with the lad from Cheltenham taking control of the table thanks to a fantastic long red before stopping one shy of recording the only century of the match.
That will not matter to snooker's Rookie of the Year, who told of his nerves after the victory.
"I was nervous at the end so it was nice to win in one visit," said Lisowski.
"I played a kamikaze shot early in the break going into the pack of reds, and then played a bad shot on 50 and had to pot a long blue, but otherwise it was a good break.
"I've had a rubbish season so far," world number 45 went on to admit.
"I came into it expecting to qualify for every event, but then I started thinking about guarding ranking points which was the wrong mentality.
"I lost five or six games in a row but at least I have stopped the rot now. I've never done well at a venue before so this week I've got no expectations, I'll just play with a smile on my face."
Lisowski will now meet the 2010 world champion Neil Robertson in the last 16, while Mark Davis set up a second round tie against Stephen Maguire with an accomplished 4-1 win over Tom Ford.
Davis, 39, recorded breaks of 64, 84, 51 and 72 en route to the first round victory, and the Sussex-born pro insisted remaining on the outside of the top 16 is not affecting his game going forward.
"It hasn't bothered me as much as people would think," he said.
"Don't get me wrong, I would love to be in the top 16, but it's not as big as it used to be because of the way the rankings work now.
"I was one frame away from making it at one of the PTC events but lost 4-3 to Anthony Hamilton. I felt a bit more pressure in the last frame, but not bundles.
"I would have knocked Ronnie O'Sullivan out but I certainly wouldn't have been chirping about that because when you compare our careers, he should be the one in the top 16.
"It has been frustrating because it is a big milestone and once you get in the top 16, who knows what can happen. I'm further away from it now but it's not playing on my mind and I'm just trying to win matches.
"I was really pleased by the way I played today, I scored well and didn't miss much. I've been working with Terry Griffiths and he has got me looking at things differently. If you are potting balls, it doesn't matter who is sitting in the other chair.
"I like this venue and it's a knowledgeable crowd. I always enjoy playing in Ireland because the players are so friendly."
Stephen Lee continued his resurgence with a 4-1 victory over Martin Gould. Lee recently reached the final of the China Open, where he lost to Mark Allen, but looked assured in beating Gould.
Ricky Walden was even more dominant, firing two century breaks as he rattled past Matthew Stevens 4-0.
Elsewhere on the day Xiao Guodong overcame the pain of a broken hand to beat Dominic Dale 4-2 to advance to the next round, while later on Fergal O'Brien was swept aside by Joe Perry 4-0 in one of the evening clashes.
Jack Lisowski 4-3 Barry Hawkins
Mark Davis 4-1 Tom Ford
Stephen Lee 4-1 Martin Gould
Ricky Walden 4-0 Matthew Stevens
Xiao Guodong 4-2 Dominic Dale
Joe Perry 4-0 Fergal O'Brien
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