US Edition The 40-year-old Scot finished with a century – his third of the match – as he clinched a 9-6 victory over the 52 year-old Essex cueman.
When Davis came through qualifying to set up the clash with Hendry it was perhaps the most eagerly anticipated of the first-round matches.
Yet Davis could not score heavily enough and that was his downfall, even though he kept pace with Hendry for much of the contest.
It was anyone's match at 6-6, but runs of 37, 40, 41 and 112 from Hendry ensured he will go on to tackle Mark Selby in the next round.
Hendry had made centuries in the first and final frames of the early-afternoon session, 115 to start with and then a 130 clearance to black, and during those big breaks he looked a fearsome player.
However, like Davis, he missed far more balls than he would have done in his heyday, which should give Selby some encouragement.
Hendry said: "I won, it's as simple as that. Snooker is torture at the moment. It's very frustrating.
"In the last frame I potted a long red and made a good break – that's what you're supposed to do, do it in one visit. It was a great atmosphere, it shows we are still popular, which is nice."
Davis was co-opted onto the board of the World Professional Billiards and Snooker Association on Friday, along with his long-time manager Barry Hearn, who should soon be confirmed as the WPBSA's new chairman.
The six-time world champion will almost certainly make a greater contribution to the game away from the table over the next couple of years than on it.
Nevertheless Davis said: "I was competitive, I felt like a player. I got a couple of kicks at bad times which didn't help.
"At times Stephen looked vulnerable, but he did make three centuries, he's still a fantastic positional player among the balls.
"It wasn't the greatest match, but at 6-6 I had a chance. He played some good frames and some ropey ones, it was a strange match."
For a while, it seemed that Jamie Cope would be waiting for the winner of Hendry's match, but Selby staged a brilliant fightback.
The 26 year-old Leicester potter was 8-4 down and staring at a dismal defeat to fellow Englishman Cope, but he reeled off five successive frames to take the match, with breaks of 67, 101, 57, 115 and a closing 73.
Peter Ebdon reeled off five frames in a row to sink Judd Trump 9-4, in another all-English battle, making breaks of 80 and 84 along the way.
Welshman Ryan Day went out of the tournament after a heavy 9-3 defeat to China's Liang Wenbo, but he almost had the consolation of a maximum 147 break.
Day cleared all the reds and blacks and an easy yellow in the 11th frame, when 8-2 behind, but was left with a tricky green along the cushion.
He made a precision pot, but his positioning on the brown was then awkward, despite the colour being on its spot, and he missed a tricky cut to break down on 125.
Australian Neil Robertson converted a 5-3 overnight lead into a 9-3 victory against England's Tom Ford.
Grand Prix champion Robertson was clinical and made breaks of 48, 64, 53 and 87 before finishing with a break of 119, and he will face John Higgins or Ricky Walden next.
Robertson said: "The Grand Prix was a little while ago so it's not as if I'm still buzzing from that. I had a week off after that and have been practising hard but I feel refreshed."
Stuart Bingham will face Stephen Maguire in round two after knocking out Joe Perry in an all-English battle. With a 6-2 lead going into the session, he completed a 9-4 victory without needing to find any 50-plus breaks.