Mercer (2-3, 0-2 Southern Conference) attempted a 42-yard field goal as the final seconds ticked off the clock, but Jagger Lieb's kick went wide left.
Western Carolina (3-2, 1-1) scored twice in the final quarter - C.J. Goodman scoring a 14-yard TD run that pulled the Catamounts to 2 1-17 - and then Newsome's run to cap a 14-play drive that started at the 9-yard line.
Troy Mitchell rushed for 79 yards and Newsome 59 as Western Carolina gained 338 yards of total offense.
Mercer led in nearly every offensive category but went scoreless in the second half after posting a 21-3 halftime lead.
Mercer's John Russ passed for 205 yards and also rushed for a touchdown.