The top-seeded Frenchman did not face a break point, winning 36 of his 41 service points.
The third-seeded Tipsarevic saved six break points to oust Belgian qualifier David Goffin 6-4, 6-2.
The seventh-seeded Croat had 15 aces. Beck was broken at 5-4 to lose the opening set before dropping the second on a tiebreaker.
Llodra, a 2010 champion, had 12 aces.