In a battle of baseline specialists it was Rubin who was the sharper at the outset, grinding out a tight first set before errors began to pile up in the second.
The 22-year-old had his shoulder looked at by a trainer during a medical time out prior to the third set but his accuracy never returned as Thompson overwhelmed him with a booming first serve and relentless counterpunching.
Next up for Sydney native Thompson is a second-round tie against Spaniard Adrian Menendez Maceiras or American Christopher Eubanks, who play their first round match on Tuesday.
Rubin was not the only American to make a first-round exit on Monday with eighth seed Tennys Sandgren losing out to Italian Paolo Lorenzi 7-6(4) 6-7(4) 6-4 at the tournament, which is played on indoor hard courts at the Nassau Veterans Memorial Coliseum. (Reporting by Rory Carroll; Editing by Peter Rutherford )