The 34-year-old shot two birdies over the first nine holes and finished with three more on the back nine to give himself a decent platform for the remainder of the tournament.
"It was a pretty solid round," Westwood said.
"It was a good day's workout and my confidence is pretty good."
"I have a long way to go but I really hit the ball pretty decent today."
Westwood, who lost out on the Abu Dhabi title which was won by German Martin Kaymer, credited his success to a new fitness regime that involves a lot of gym work.
"I've improved my fitness a great deal. I work out a lot in the gym and obviously that helps."
Haig made a steady start picking up two shots over the first nine holes, but stepped up his game to blaze four birdies over the next seven.
However, he suffered a bogey at the 639-yard 18th hole to finish on 67.
"I have a long way to go but I really hit the ball pretty decent today," Haig said.
"I putted really well. I am looking forward to a steady week."
The South African, however, said the windy conditions at the course tested his patience.
"It's a tough struggle out there, especially with the conditions as they are, windy, and there are a lot of good players out there," said Haig.
England's Paul Broadhurst, the Swedish trio of Alexander Noren, Johan Edfors and Henrik Stenson, Aussie Adam Scott, Spaniard Sergio Garcia and German Marcel Siem were in joint second place on 69.
Garcia, who finished second at last year's Open Championship, was left ruing some poor putting towards the end of his round, as he had an eagle putt on the 16th which turned into a par, and then missed an easy putt for birdie on the final hole.
Scott, world number eight, also missed a birdie putt on the 18th but remains in striking distance to secure the title he first won in 2002.