Former Wimbledon Junior champion Rubin, 23, beating fellow American Michael Mmoh 6-3, 6-4 in the first qualification round and followed it up with a three-set win over Roberto Quiroz of Ecuador in the round of 64. He came from a set down to win 4-6, 6-1, 6-2.
Dudi Sela, ranked 157, lost a three-set match against Pedro Menéndez of Spain. Israel’s no. 1 took the first set 6-1 before the Spaniard levelled things up by winning the second set 6-0. Menendez broke serve in the deciding set to progress 6-4.
Deniz Khazaniuk of Israel also missed out on a spot at Wimbledon after losing in straight sets against Fangzhou
Camila Giorgi of Italy was in action at the Eastbourne International on her return to action following three months out with an injury.
But she bowed out in the opening round after a three-set thriller against Hsieh Su-Wei of Tapei.
Diego Schwartzman has been confirmed as the competition's 24th seed in the Men's Singles for the grand slam tournament which gets under way on Monday.