Ram took a seesaw 7-6 (7-3), 7-5 decision over Baker in a match that took nearly 2 hours.
Baker was good on 76 percent of his first serves but, when he missed, Ram pounced on the second serves, willing almost two-thirds of the points in those situations. That helped Ram post two breaks in each set.
Paul Capdeville also needed about 2 hours to get by Igor Kunitsyn 6-4, 7-6 (7-5).
Capdeville lost only seven points on serve in the first set and fought off 5-of-6 break points in the second.
Flavio Cipolla rolled by Jack Sock 6-3, 6-1 behind five service breaks. Cipolla dropped 16 points on serve in the match and won 60 percent of the points overall.
Celebrity Families of 2014 [PHOTOS]