The promising 19-year-old from Leeds scored a 5-3 victory to reach the last 16 of the event and earn a meeting with the eighth seed, Nigel Bond. In the process, Hunter also impressed Davis, a player well-qualified to assess the relative merits of the game's up-and-coming young talents.
"I think the jury is out on any player until they win a tournament or two, but Paul certainly deserves his label as a strong prospect," said Davis. "He looks confident and he knows what he's doing around the table."
Hunter, quoted as an odds-on favourite by the bookmakers, fell 2-1 behind before racing through the following three frames in only 38 minutes thanks to breaks of 87, 72 and 56. Davis doggedly salvaged the next only for Hunter to apply the finishing touches to an accomplished performance by potting the blue to a distant baulk pocket in frame eight.
"It's a tremendous result for me, especially because that's the first time I have ever played Steve," said Hunter, the world No 43. "I was nervous before the start but once I'd got a frame under my belt I knew I could do something."
Hunter will now be hoping to repeat the 5-1 victory over Bond which launched his record-breaking run in the 1996 Regal Welsh when, at only 17 years and four months old, he became the youngest player ever to figure in the semi-finals of a world-ranking tournament.
Even in defeat Davis, who in a fortnight begins the defence of his Benson and Hedges Masters title, gained encouragement from an improvement on some dismal displays of late.
"I have been very disheartened with my form in practice and in matches all season, but that was a lot better," he said. "Watching a slow-motion replay of myself at a European League match a couple of weeks ago I realised I wasn't cueing well. I have remodelled by cue action a bit and I have started to make some headway. Frustrations have been replaced by optimism."
Mark King, runner-up to Stephen Hendry in last year's Welsh Open, joined Hunter in the last 16 with a 5-2 win over Tony Chappel, the Swansea professional responsible for Ken Doherty's surprise second-round exit. King, who pinched the first frame on the black, with an excellent 66 clearance, added breaks of 67 and 86 in leading 4-2 before he sealed victory by potting green to pink in a tight seventh.
The Romford left-hander now tackles another Welsh rival in Dominic Dale, the Grand Prix champion, for an appearance in the quarter-finals. Jamie Burnett, shock conqueror of Stephen Hendry in the second round, retained the winning habit on Sunday night.
The Scot secured a last 16 meeting with Stephen Lee when he progressed with a 5-3 victory over Joe Perry. Against Hendry, Burnett was forced to rally from 4-2 down to win 5-4 but it was a different story against Perry. He always held the upper hand after moving 3-1 ahead with runs of 36, 44, 35 and 71 in the early stages.
"With so many of the top players going out I feel capable of doing something," said Burnett. "Obviously, when you've beaten someone like Stephen, it gives you a tremendous amount of confidence and I'm really determined to capitalise on it."
Burnett's fellow countryman Graeme Dott was also in the groove as he set a personal best and put himself in line for a pounds 5,000 bonus, for the highest televised break, during a 5-2 victory over Steve James. The 20- year-old from Larkhall, near Glasgow who had already ousted the 12th seed, James Wattana, in the previous round, had a 142 clearance.Reuse content