Haws, a 6-foot-5 guard, scored 20 points to help the Cougars beat Texas-El Paso Paso 83-77 on Saturday night.
"Guys stepped up tonight and helped us, for sure," Haws said. "I just treat every game the same."
Haws came through from the start, but added two clutch points from the free-throw line with 22 seconds left, giving the Cougars (16-1) a six-point lead.
"Those are the situations you kind of dream about, being at the line with the ball in your hands," Haws said.
UTEP (10-4) led early and kept it close, but couldn't regain control after BYU took the lead Jonathan Tavernari's 3-pointer with 1:26 left in the first half.
Tavernari, who had 19 points before fouling out with 1:35 left, said the Cougars stepped up in a physical game that gave them 28 shots from the free-throw line.
"We want teams to kind of press us," Tavernarisaid. "We just beat a really good UTEP team. Most likely they will be dancing in March. They are really good."
BYU coach Dave Rose said his team struggled early under pressure from UTEP but seemed to return to form after taking the lead late in the first half.
"We got on a that little bit of a run and then we started looking a little bit more like ourselves and then in the second half we played really well," Rose said.
BYU shot just 48 percent from the field in the first half, before hitting 62 percent of their shots in the second half.
Rose said he did not have a timeline for Fredette's return, adding that it was largely dependent on his leading scorer simply feeling better.
UTEP coach Tony Barbee was upset with his team's fundamental play.
"They executed when they needed to execute their plays to a T, we didn't," Barbee said. "Defensively they got the stops when they need them. We broke down offensively."
Barbee said some of his guys even appeared to forget plays.
"I don't know if I can make our plays any simpler and we've got guys who can't remember their plays," Barbee said.
After leading 37-34 at the half, the Cougars did their best to open the game up early in the second half, taking a 10 point lead 17:11 left. But Polk kept the Miners close with a quick pair of 3-pointers.
UTEP shot 71 percent from the line, but missed 11 free shots, including a string of three free throws that would have given UTEP a narrow lead with less than 7 minutes in the game.