Trump, who was forced to change his extravagant footwear during the match due to a lack of grip, looked to be sliding to a shock first-round defeat after Hawkins rattled off three successive frames from 3-2 down to put himself within sight of the win.
However, Trump battled back with a 105 break before edging a tension-filled 10th frame – where Hawkins missed a couple of straightforward-looking pots with victory within his grasp – to send the match to a decider.
Relieved to still be in contention, the Bristolian rattled off a brilliant break of 107 in the final frame to claim a 6-5 victory and set up a quarter-final meeting with Scotland’s Graeme Dott.
Trump feared the worst before Hawkins let him back in with the missed shots in the 10th frame.
Asked if he felt he was heading out, Trump said: “Yeah, I didn’t really see the angle he had on the first black when he was playing for the yellow, but it looked pretty easy from where I was and the second one I never thought he was going to miss.
“Whoever you play here is going to be a tough game, Barry played really well so hopefully that stands me in good stead for the rest of the tournament.”
Trump’s bid did not appear to be helped at the outset by his choice of footwear.
The 23-year-old’s stud-covered ‘Rollerboy Spikes’ captured plenty of attention but they were new to Trump and he found them ill-suited to the demands of playing on carpet in Alexandra Palace.
Not that it has put him off wearing them in the future.
He said of his new shoes: “I thought it was time for a change. I’ve had my other ones for a long time. I went out for the first two frames and tried them on and I was sliding around out there and had to take them off.
“I was all right in the practice room but as soon as I went out there I just started sliding around.
“We’re going to have to make a few adjustments so I can wear them.
“It’s just a little bit different, I like to stand out now and again.”
Having reached the semi-finals last year, Trump is widely fancied to go all the way at the Masters.
However, he was keen to play down the tag of favourite and insists he is still learning his trade.
“I still don’t see myself as the favourite. Every tournament I play in I see John Higgins as the favourite.
“I think John Higgins is proven and I’ve still only won three tournaments,” he said.
“I go into every tournament full of confidence but I’ve still got a lot to learn and I’m still learning today.”