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 Liu in the Ladies qualifiers.
Camila Giorgi of Italy was in action at the Eastbourne International on her return to action following three months out with an injury.