Andy played better behind the first serve but the second let him down, dropping serve five times from ten chances given to Viola and responding with five breaks from 11 chances, unable to steal the opponent's serve one more time before the tie break in the final set and hitting the exit door after first back-to-back triumphs since September past year.
Murray dropped down to the Challenger Tour for the first time since 2005 in a bid to improve his fitness following hip resurfacing surgery in January, which threatened to end his stellar career.
The 32 year-old Scot went out at the third round stage in losing to Italy's Viola 3-6, 6-4, 7-6 in two hours and 43 minutes on Thursday night.
The Briton was beaten 3-6 6-4 7-6 (7-3) in the Challenger Tour event after hitting a double fault on match point in the final-set tie-break.
He struggled physically during the third set, receiving treatment on his left thigh during two medical time-outs which he said was for "cramping".
"I'm cramping. Very exhausted", Murray said. I played two competitive matches.
The Brit started a singles comeback at ATP Masters 1000 tournament the Western & Southern Open before making a swift exit from the Winston-Salem Open.
Murray, who played in the Mallorca Challenger event rather than compete in doubles at Flushing Meadows, is set to play in the Zhuzai Championships in September, then European and China Opens the following month.
Clemson RB Travis Etienne explodes for 90-yard TD run
Lawrence cashed in five plays later with a 6-yard zone read keeper to give Clemson its first of many early leads this season. That said, Higgins did put up one of the best plays of the night on a 62-yard catch-and-run touchdown from Lawrence.