The lead changed hands several times during the round but it was the world number seven who finally prevailed with a two-under-par 70, which included four birdies and two bogeys, for a final total of 17-under.
"Lucas played incredible golf," Rose told reporters. "It was the first time I had the chance to play with him. I was thoroughly impressed, not just his game but his temperament and how he is as a person.
"When you separate yourself from the field like we did, it's probably a tough one for him to lose. But he didn't lose it, just both of us played incredibly well and separated from the field.
"I'm very happy to get the job done. I had a chance to win in Napa last week, I was tied for the lead going down the 10th hole and let that one flitter away a little bit. I wanted to hang onto this one."
The duo came into the final round four strokes clear of the chasing pack and maintained that gap while fighting for the title.
Bjerregaard, who picked up his fourth top-10 finish in the last month, saw his chances fade with a double bogey on the par-four 14th. He carded five birdies and two bogeys during his round of 69.
"It was fun to battle with Justin these last two days," said Bjerregaard. "It's guys like him that I want to go out and compete against, and at least I gave him a little bit of a scare.
"That double bogey on 14 really ruined it for me but all in all, happy the way I've played.
"The last time I was out in the final group on a Sunday, I shot 89. So 20 shots better today, I'll take that."
South Korean Lee Soo-min shot a 64 to surge up the leaderboard for a share of third place with British Masters winner Matthew Fitzpatrick, American Patrick Reed and Australian Jason Scrivener -- all on 11-under.
(Reporting by Sudipto Ganguly in Mumbai; editing by Peter Rutherford)
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