After blazing through the first set, the 195-ranked Rao faced tough resistance from the 20-year-old Klaschka in the second.
But it was Rao, India's number two tennis player after Sania Mirza, who prevailed in the tiebreaker.

Although ranked only 296, the 18-year-old Glatch leads Rao 2-0 in career meetings, having beaten her in 2004 and in the final of the $25,000 Southlake, Texas tournament in July this year.
Rao had bowed out of last month's Sunfeast Open in the second round with a 3-6, 2-6 loss to Britain's Anne Keothavong.