Englishman Westwood, who cantered to a seven-stroke win last year, mixed seven birdies with one bogey in the $3 million (2 million pound) event at the Kuala Lumpur Golf and Country Club that is co-sanctioned by the European and Asian tours.
"I'll take that. I putted very nicely and started the ball on line well," said Westwood who featured prominently at the Dubai Desert Classic last week and also won the Malaysian crown in 1997.
"I left a couple short in the middle when I was fooled by the grain but overall I'm very happy," he told reporters. "It's probably the toughest I've ever seen this golf course play."
Former U.S. Open champion McDowell matched Westwood's seven- birdie haul after also starting on the back nine. Co-incidentally his only dropped shot also came at the par-four sixth.
"I'm pretty happy," said the Northern Irishman who finished tied for ninth with Westwood in Dubai. "I hit the ball great today, drove it well and gave myself a lot of looks for birdie.
"I've liked the way this golf course looks from the start and I enjoyed playing it this morning with good company from the boys."
Local hope Danny Chia carded a 67 to share third spot with Englishman Tommy Fleetwood and Kang Sung-Hoon of South Korea.
Europe's 2014 Ryder Cup captain Paul McGinley went round in 69 and was tied for 10th place.
Spaniard Miguel Angel Jimenez and Asian Tour Order of Merit winner David Lipsky of the United States started with 72s.
(Writing by Sudipto Ganguly, editing by Tony Jimenez)
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