Ridnour, an Oregon junior guard who averaged just under 20 points and seven assists per game this season, crashed into Jacobson as he was sizing up a three-pointer with the game tied at 58-58. Jacobson missed his first attempt from the line but hit the next two.
"The shot clock was running down," Jacobson said. "I just took the shot. Luke was up on me and fouled me. I missed the first one, it felt good, and it went off the back rim.
"I can't do anything about that. I just shoot them like I shoot in practice. I didn't think anything more of it and I made the last two."
Oregon (23-10) got two good looks at the basket on its final possesion, but Davis missed a three-pointer from the left wing with five seconds to go. The ball was tapped out to Davis, who was behind the line but missed again as time expired.
"They hit some shots down the stretch. We had some great looks there at the end of the game, but the ball didn't fall in," Oregon Coach Ernie Kent said.
Jacobson admitted to a few anxious moments.
"It looked like both shots were going in," he said. "It was happening quick, so I didn't think about it too much. I was just praying that someone would get a long rebound and hoping someone would keep it in the air long enough that the clock would run out."
Jacobson led Utah (25-7) with a season-high 23 points, making eight of 14 shots including five of nine from three-point range. Marc Jackson added 13 off the bench for the Utes before fouling out.
The contributions from Jacobson and Jackson were key as the Utes were without senior forward Britton Johnsen, who missed the game while recovering from mononucleosis. A member of the 1998 Final Four team, Johnsen averaged 11.6 points and 6.7 rebounds this season.
Utah also saw Tim Frost and Cameron Koford foul out and was forced to play with makeshift lineups throughout the second half.
"I credit the players," Utah Coach Rick Majerus said. "The players did a great job of hanging in there. We had lineups we had never played, obviously necessitated by the absence of Britton and the foul trouble, which compounded the problem. I thought the guys did a marvelous job."
Ridnour, who could opt to turn professional, had just 13 points, missing nine of his 12 shots. For the first time all season, he did not make a three-pointer.
"We've got to give them a lot of credit but I didn't hit shots that I make normally," Ridnour said. "Other guys stepped up but we just didn't get it done today."
"Our plan was to double team off the on-ball picks," Jackson said of the game plan against Ridnour. "Make him shoot a tough shot around the perimeter. We did that pretty good in the first half."
Utah, which improved to 9-1 in opening-round games under Majerus, advanced to face Kentucky in the second round on Sunday.
The Ducks, ranked as high as fifth in the country this season, were the Pac-10 tournament champions but failed to build on their impressive run in this tournament last year.
"It was a great run for this basketball team and a great season," Kent said. "I thought we did a nice job starting the game, but Utah hit some threes and the tempo was certainly in their favor."
Oregon looked like it was going to blow Utah out early, opening the game with a 9-0 run. But the Utes stormed back and were within 11-10 following a three-pointer by Jacobson with 12:28 left in the half.
A three-pointer by Jackson gave Utah its first lead of the game, 15-14, midway through the opening half. The Utes seized a 26-18 lead with four minutes to go on two free throws by Jackson.
Two free throws by Ridnour with 39 seconds left in the half sliced Oregon's deficit to 30-27 at the break.