Day finished with an 8-under 64 after completing the final two holes at Greystone's Founders Course. He was scheduled to tee off for the second round a few hours after completing the first with a birdie on No. 18.
Toms had six birdies and a bogey for a 67.
Two-time winner Bernhard Langer, who has won a record 10 senior majors, finished at 69.
Day is seeking his first win on the senior tour. His only PGA Tour victory came in 1999.