"The funny thing is that I played much better at the Crucible when I lost than I did out there," Henry said. "The run of the ball I had tonight was amazing. Every time I made a mistake I seemed to get away with it.
"There were times during the match when I couldn't help getting a little bit embarrassed with all the good luck I was having."
Henry, the world No 40, held a 3-1 lead at the mid-session interval but then somehow missed a straightforward black to move 4-1 ahead and when a 50 break carried Parrott onto level terms at 3-3, the former World and UK champion appeared to have swung the momentum in his favour.
Parrott also led 41-11 in frame seven but Henry, aided by a well-timed fluke snooker, eventually snatched it on the pink prior to comfortably winning the eighth as he set up a second-round meeting with Gary Wilkinson.
Malta's Tony Drago overcame the experienced Welshman Wayne Jones. Drago, runner up at the International Open in Aberdeen last month, now plays Ian McCulloch of Preston.
Alan McManus avoided a third successive first-round defeat when he scored a 5-2 victory over Tony Jones.