Trailing 23-14 in the third quarter, the Vandals failed to convert on fourth-and-5 from their 38. The Bobcats took advantage, twice converting on fourth down, including Tim Gay's 20-yard scoring run.
In the fourth quarter, Jones faked a keeper and found Terrence Franks alone for a 67-yard score and a comfortable 37-14 lead.
Texas State took a 23-14 lead as the first half ended when Isaiah Battle made a one-handed, 4-yard reception in the corner of the end zone.
Idaho's James Baker rushed for 114 yards and a TD. Taylor Davis, who started the year as the third-string QB, passed for two touchdowns.
Texas State (6-3) won its third consecutive game to become bowl-eligible. Idaho (1-8), dropping its fourth straight, joins Texas State next season in the Sun Belt.