Webster reached 14 under, one clear of countryman Richard Finch, who followed up a course-record 63 with a 71.
Wales’ Bradley Dredge carded a 71 for 12 under alongside England’s Simon Khan, who shot 68.
On 11 under were Scot David Drysdale, England’s Stuart Little and Jamie Spence and Ireland’s Gary Murphy but Paul Broadhurst (75) slipped back.
Webster fired five birdies in a row after the turn to ignite his push, and though he had two bogeys and a birdie in the last five holes, he finished better then Finch.
The 27-year-old from Hull bogeyed the 15th and last, where he narrowly avoided going in the lake. Finch, chasing his first win after only nine Tour starts, said: “I enjoyed it out there. It was a slightly disappointing back nine really, but I’m still not out of it.”
Spence, the European Tour’s tournament committee chairman, lost his card last year and was close to resigning after a bad start to this season.
In Dubai in March he said: “I’d like to pack up and do something that I enjoy. Got any ideas?
“Being chairman is a pretty thankless task. Everyone’s moaning at you. There’s too much moaning, to be honest.”
But after a best-of-the-day 65 he said: “I’ve asked some serious questions of myself. I don’t want to be a good chairman and crap golfer, but I’ve decided not to quit.
“I’ve had a rotten year and a half, but when I’m playing I’ve just got to concentrate on playing and when players come to me about something I’ll tell them to put it in a letter.
“Even last night I had some calls about our next meeting and it’s no coincidence I haven’t played as well since taking over from Mark.
“The last three events last year, when I should have been thinking about nothing other than keeping my card, my mind was elsewhere.”