The two most important of Jones' points came on a putback with 20 seconds left after returning from a knee injury. The shot provided the final margin of victory for the Bears.
"I couldn't let my team down," said Jones, a sophomore. "I didn't want to use my knee as a crutch. I just wanted to go back in and do what I could do to help my team win."
The other star for Baylor was a guy more than a foot shorter.
Point guard Pierre Jackson blocked Brandon Davies' 3-point shot at the buzzer that might have forced overtime.
"You don't expect your 5-9, 5-10 point guard to do that, but Pierre is really athletic," Baylor coach Scott Drew said. "And the thing about him is he's a competitor. He didn't want Davies to get a shot to (force) overtime."
The 6-foot-9 Davies, who scored 18 points and dominated the boards (13) for BYU, was as shocked as anyone.
"I had no idea where he came from," Davies said. "I didn't see him at all."
Baylor is off to the third 9-0 start in school history and best under Drew.
It wasn't easy.
BYU (8-3) led by as many as 13 points in the first half thanks to 9-0 and 10-0 runs, and a huge advantage on the boards.
After 8½ minutes, BYU held a 14-0 rebounding advantage
"You've got to credit BYU's team for playing outstanding in the first half," Drew said. "They got multiple good shot attempts and that was because of their heart and their toughness.
"A lot of times people talk about BYU's great transition game and great scoring, but they're a tough team. It's a good group of guys then the crowd got them going."
But Drew was proud of the way his team showed resilience the final four minutes after the Cougars came charging back.
"We got stops and rebounds," Drew said.
Baylor regained the lead 65-64 after six straight points by Jones, then surged ahead 79-70.
But BYU fought back behind the play of freshman guard Matt Carlino.
Carlino was making his BYU debut after sitting out last year after transferring from UCLA.
While he didn't put up numbers like last year's national player of the year Jimmer Fredette, the shoes he ultimately is expected to fill, he definitely turned heads.
"The scouting report we got didn't do him justice," Drew said. "We knew he was a good shooter, but we didn't know he could make tough shots like that. If he continues to do that all year long, it gives BYU another weapon."
Carlino made 7 of 14 shots, including 4 of 8 from 3-point range, to finish with 18 off the bench.
But Carlino also committed four turnovers, including one as BYU had pulled within 84-83 on a jumper by Charles Abouo.
"Carlino played well but he just needs some experience," BYU coach Dave Rose said.
BYU won the battle on the boards, 44-31 and outscored Baylor 41-24 in the paint.
Jones was too much in the second half, when he scored 16 of his 28 points and grabbed five of his eight rebounds.
Plus, the Bears were almost unstoppable from 3-point range. Brady Heslip hit six 3-pointers and Baylor made 13 of 25 overall.
Heslip finished with 18 points, while Jackson added 13.
Davies had 18 points, 13 rebounds, a block and a steal for the Cougars.
Charles Abouo added 17 points on 7-of-10 shooting for BYU, and Noah Hartsock scored 15.
West Coast Conference commissioner Jamie Janinovich was in attendance to see the Cougars, the league's newest member. And Utah Jazz general manager Kevin O'Connor was in the arena to check out several Baylor players, including sophomore Jones and freshman Quincy Miller, who were on the preseason Naismith Trophy watch list.
Jones didn't disappoint, even if he gave coaches a scare when he knocked knees and had to be helped off the court with 1:26 remaining.
"Some players come back after an injury and they limp around," Drew said. "He showed his toughness."
Baylor became only the second non-conference opponent to win in Provo against BYU in the last 50 games. No. 6 Wake Forest was the other in 2009.
"It's a tough place to play no matter what league they're in," Drew said of the Cougars, who were being courted to join the Big 12 earlier this year. "That's why we wanted to come up here. We walked out a better team knowing more about ourselves in doing so."