Cabrera-Bello, who also led last week's Abu Dhabi Championship after two rounds before finishing fourth, dropped two shots in the last six holes to card a 73.
That opened the door for Webster, who got off to a poor start and was two over after five holes but rallied to hit the remaining 13 in four under, carding 70 to join Cabrera-Bello on 12 under par.
Frenchman Adrien Saddier, who hit a third-round 64, Denmark's Thorbjorn Olesen and South Africa's Thomas Aiken were a shot adrift of the leaders.
"It was a tougher day today, things did not go as great as they have been so far," Cabrera-Bello said on the European Tour website (www.europeantour.com).
"I still feel as though I played okay, I just did not manage to score as well. It was tough with the wind, I didn't quite make the putts and struggled here and there with my chipping, but overall I got the not-so-good round out of the way and I am still in a fantastic position going into Saturday."
Webster, who became the first player to start a European Tour event with an albatross on Wednesday, boosted his chances of a third tour title after recovering from an early stumble.
"I hit it really well on the range and I think I got a bit cocky on the course and hit so many bad shots the first six or seven holes; it was like I had never played golf before," he said.