He scored on an 11-yard run with 11:20 remaining in the second quarter, giving the Texans a 14-10 lead.
Singletary has 10 carries for 64 yards.
The Texans have yet to punt. They turned it over on downs after getting inside the red zone on their first drive.
C.J. Stroud threw a 20-yard touchdown pass to Dalton Schultz on the Texans' second drive.