But compatriots Gordon Reid and Jordanne Whiley both suffered singles losses in New York.
Lapthorne defeated American Nick Taylor 6-4 6-3 in the first of his three round-robin matches.
But Reid lost 6-4 3-6 6-3 to Argentina’s Gustavo Fernandez and Whiley fell 6-1 6-4 to Marjolein Buis of the Netherlands.
World number three Lapthorne made a confident start against Taylor, going into a 5-2 lead before wrapping up the set and then breaking Taylor’s serve midway through the second set to secure victory.
“It’s always tough in the first match of a Grand Slam and I’m really pleased to get a win under my belt, especially in those hot conditions in the middle of the day,” said Lapthorne, who will face defending champion Lucas Sithole of South Africa on Friday.
“I didn’t feel like I got out of first gear and was over-hitting a bit, but I found my rhythm more as the match went on and I’m confident I can improve my play and take that into the rest of the week.”
Both Reid and Whiley will be in action on Friday in the doubles, with Whiley and her Japanese partner Yui Kamiji starting their bid to complete a clean sweep of all four Grand Slam women’s doubles titles in the same calendar year.