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.
"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 U.S., on his 25th birthday, shot 66 to be 8 under. He planned nothing special for his birthday except a nice dinner on Friday.
Henrik Stenson improved from his opening 70 with a 67, to lie at 7 under with Thai Kiradech Aphibarnrat (68), Indian Sujjan Singh (69) and Australian Andrew Dodt (65).