Cabrera-Bello shot 1-over-par 73 and was caught by Webster, who carded 70 at Doha Golf Club for three-round totals of 12-under 204.
They are only one stroke ahead of Adrien Saddier, the biggest mover with six birdies in his round of 64, Thomas Aiken (70) and Thorbjorn Olesen (68) on a packed leaderboard.
Cabrera-Bello, chasing his first win on the European Tour in two years, began the day leading by two on 13 under, and went three shots clear with a birdie at the second hole.
However, he dropped shots on Nos. 6 for a second consecutive day, 13 and 15.
“I didn’t think I played that bad,” Cabrera-Bello said. “On the back nine, I didn’t quite make the birdie putts as I did yesterday, but overall, I could have won it today.”
Webster, looking to win for a first time in more than six years, bogeyed the fourth and fifth holes to fall to 8-under then played the rest of the way in 4-under. On the par-5 18th, he pitched to 10 feet for a birdie putt and outright lead but missed.
Ernie Els (71, 2-under) and Luke Donald (74,
1under) couldn’t stay in contention, and U.S. PGA Championship winner Jason Dufner slumped to 3 over following his round of 78 that included seven bogeys and one birdie.
LPGA TOUR: In Paradise Island, Bahamas, Jessica Korda took the second-round lead in the season-opening Bahamas LPGA Classic, birdieing four of her last seven holes in high wind for 7-under-par 66.
The 20-year-old Korda has an 11-under 135 total on Atlantis Resort’s Ocean Club course.
Paula Creamer, playing alongside Korda, is a stroke back after 65.
Creamer drove left on the first hole and three-putted from 7 feet. She birdied 10 of the last 17 holes.
Lydia Ko, the 16-year-old who shared the first-round lead with Meena Lee, is three strokes behind at 8-under after 70.
Lee had 76 to drop to 2- under.