"The most important thing tonight is we got better as a team," he said. "As the game went on, I thought we got better."
With seven minutes left in the first half, Prairie View had battled BYU to a 19-19 tie.
Rogers scored seven points in the final 5:15 of the half, however, and the Cougars built a 34-25 lead.
BYU's switch to a zone defense helped ignite the 15-6 surge.
"The zone, tonight, was good for us," Rose said. "If we can rebound out of it, we'll probably play it more."
In the second half, the Cougars were unstoppable.
They outscored the Panthers, 56-26. They shot 67.9 percent from the field, including 8-for-12 from the three-point line.
"It was a terribly played second half," said Prairie View coach Byron Rimm II. "Our transition defense was terrible, we didn't do the little things and we gave up. It was a great basketball game by BYU, and we didn't produce in the second half."
Still, BYU owned only a 41-32 lead with 16 minutes left.
Prairie View remained in the game at least until an 18-0 blitz over the next eight minutes that gave the Cougars a 59-32 lead.
According to Brandon Davies, who finished with 13 points and eight rebounds in a team-high 26 minutes, BYU's sustained effort was the key.
"We always try to play hard," he said. "It doesn't matter who we're playing, you don't get better if you don't play hard.
Three other Cougars joined Rogers and Davies in double figures: Charles Abouo (13 points), Noah Hartsock (12) and Anson Winder (11).
BYU's bench outscored Prairie View's nonstarters 41-19 in the second-round game of the Chicago Invitational Challenge.
The Cougars play Nevada in suburban Chicago on Friday, with a matchup against either Bradley or Wisconsin coming Saturday.
BYU 90,Prairie View 51
R Stephen Rogers scores 18 points in only 12 minutes.
• The Cougars dominate the second half, shooting 67.9 percent from the field and outscoring the Panthers56-26.