The seventh-seeded Hewitt, who was runner-up two weeks ago on grass in Newport, Rhode Island, was one of three seeded players to finish his match before a pair of evening rain delays. Play eventually was suspended until Wednesday.
The victory speaks a lot as Sijsling had made finals at Australian Open and Vasselin had appeared in the Wimbledon semifinals.
Defending US Open champion Samantha Stosur of Australia and Spanish fourth seed David Ferrer advanced at the US Open with straight-set victories on Friday.
Two-time champion Sam Querrey won his opening match in the Farmers Classic, beating Igor Sijsling of the Netherlands 6-2, 6-2 on Wednesday at the Los Angeles Tennis Center.