Garcia, who finished fourth at the same event last year and is trying for his first title this year, produced a bogey-free round which included an ace on the 236-yard eighth hole.
The Spaniard was playing alongside his new girlfriend Katharina Bohem, who competed at college level in the US.
"The hole in one was a little bit of an extra bonus," said Garcia, who added it was his 10th. "I got lucky with the contours on the green. Making a hole in one is always a funny and amazing feeling.
"We can't see the hole from the tee because the pin is on the tier. I was calling it to go in, one of those things that you do, not really thinking it's going to go in. But I've seen the past couple of years guys hit over there on the right and it comes quite close to the pin.
"I was trying to hit it probably about five yards farther left than what I actually hit it but when it started rolling down the hill, I thought, you know, it's probably going to end up close.
US Open champion Rose followed a birdie on the second hole with a bogey on the third, and came back to sink two birdies and eagle the 11th for a 68 in the Asian Tour event at Amata Spring Country Club.
Their two-round tally was at 11-under-par 133, two strokes ahead of India's Anirban Lahiri (64), France's Alexander Levy (65), and Germany's Alex Cejka (71), the first-round leader.
"I had a bit of a hot spell from nine, 10, 11 and 12," Rose said. "Other than that, I found the greens more difficult this afternoon, a bit more grainy, more than yesterday."
Rickie Fowler of the US, on his 25th birthday, shot 66 to be 8 under.
Henrik Stenson improved from his opening 70 with a 67, to lie at 7 under with Thailand's Kiradech Aphibarnrat (68), Indian Sujjan Singh (69) and Australian Andrew Dodt (65).