Former world number one Westwood led by four strokes overnight but could only manage a 71 in sweltering conditions at the Kuala Lumpur Golf and Country Club after bogeying the last for a three-day total of 14-under.
Westwood, chasing his first win since claiming the 2012 Nordea Masters in Sweden, mixed three birdies with two dropped shots on Saturday as he failed to match the form shown in his opening rounds of 65 and 66.
"It was tricky out there," Westwood told reporters. "I didn't play as well as I did the first two days, but there were some difficult flags and it was really hot.
"That's as hot as I've been on a golf course for quite some time. It was a real grind, but I'm leading going into the last round so I'm quite happy with that."
Sullivan, looking for his first victory on tour, climbed up the leaderboard to move three strokes ahead of France's Julien Quesne in third on 10-under. Belgian Nicolas Colsaerts was a shot further back in fourth spot.
The Englishman, ranked 226th in the world, gained seven shots against a lone bogey on the fourth to make rapid inroads into his compatriot's advantage.
"I only made one mistake but I got it back straight away. I'm delighted with the way I finished," the 27-year-old Sullivan said.
"I felt myself getting a bit tired coming up 15 and 16. I made a couple of sloppy swings but I didn't drop any shots. I holed a good putt on 16 to keep the momentum going."
Spain's Pablo Larrazabal, who had to jump into a lake to escape a swarm of hornets on Friday, had a less eventful round of 70 for a share of the 23rd place in the $2.75 million Asian Tour co-sanctioned event.
- Sports & Recreation