Jones scored the final eight points for the Bengals (4-3) who closed the game on a 27-11 run to erase a 14-point deficit against the Broncos (3-6) who had won three of their last four games, but went scoreless over the final 2 minutes, 46 seconds.
The 6-foot-11 junior center scored 14 points, with all five of his field goals in the paint, during the stretch. Jared Stutzman set up the winning basket on his drive into the paint that found Jones for the easy layup for the 67-66 lead.
Tahj Eaddy, who led the Broncos with 17 points, missed an off-balance 12-foot jumper with 4 seconds left and Jones made 1 of 2 from the free-throw line.
The Broncos had one last chance, but Trey Wertz, who had 13 points, never got off a shot after the ball was inbounded in the backcourt with 2 seconds remaining.
No other Bengal scored in double digits. Leading scorer Brandon Boyd (17.3 points per game) was held to nine points on 4-for-11 from the field.
Eaddy kick-started the second half, which began with the Broncos trailing by five. He scored 10 straight during a 26-7 run to open the half that saw the Bengals hit only 2 of 17 from the field.
But after the Broncos built a 55-41 lead with 10:26 left, the Bengals scored nine in a row and slowly took control.
Keshawn Justice had 12 points and Henrik Jadersten had 10 for the Broncos who shot 45 percent from the floor.
Despite shooting just 37-percent from the field, the Bengals took advantage of Broncos miscues, scoring 18 points off 14 turnovers while turning it over only five times.
Neither team led by more than three until the final 8 minutes of the opening half.
Boyd keyed an 8-0 run with a pair of baskets, giving the Bengals a 27-19 advantage.
Santa Clara's freshmen then scored the next eight on an Ezekiel Richards dunk, Justice 3-pointer, Wertz driving layup and Justice free throw.
But Idaho State scored five points in the final 34 seconds to take a 34-29 lead into the locker room.
• The Bengals, who play in the Big Sky Conference, hold a 3-2 series lead over the Broncos. The home team claimed the first four games in the series.
• For the fourth-straight game, the Broncos had only eight scholarship players available due to injury. Fallou Ndoye is the latest addition to the list. He suffered a torn tendon in his foot against San Jose State (Nov. 24). Ndoye and KJ Feagin (broken hand) are out indefinitely. Juan Ducasse (knee) is out for the year.
• Starting center Ezekiel Richards picked up two fouls in the opening 1:30 of the game and only played 13 minutes in the game.
• Josh Martin pulled down 11 rebounds, his fourth-straight game with double digit rebounds.
• The Broncos won the rebounding battle in the last three games, but were even with the Bengals at 36 apiece
• The Broncos have a quick turnaround. They face Sonoma State at 2 p.m. Sunday in Leavey Center.