Allen's 8-yard TD pass to Austin Conway in the third quarter moved him into tenth place in career passing yards with 4,131. Earlier he moved into tenth on the career total offense chart with 4,738 yards.
Damian Williams found Elijah King on a 5-yard scoring pass with 3:11 remaining in the first half to pull Texas State (1-4) within 14-10, but Tyler Hall answered with a 95-yard kick return - his second TD return in as many games - to put Wyoming up 21-10.
Williams was 10 of 19 passing for a season-low 91 yards for the Bobcats. Willie Jones III relieved and ran for 57 yards on five carries.