Kunitsyn came from behind to down fellow Russian Igor Andreev
6-7 (6-8), 6-4, 6-2.
Lopez beat fellow Spaniard Guillermo Garcia-Lopez 6-3, 6-4.
Zeng, of China, rallied to overcome Dudi Sela of Israel 2-6, 6-1, 6-4 and Beck, of Germany, advanced after his opponent, Jose Acasuso, quit in the second set with a left knee injury.
Spaniard Rafael Nadal and Serbian Novak Djokovic are the 1-2 seeds in the tournament.