Carlos Emory also had 19 points, and Devoe Joseph and Garrett Sim scored 15 each for the Ducks (24-9), who rallied from a 15-point deficit in the first half to advance to the quarterfinals and a game against Pac-12 rival Washington in Seattle on Tuesday.
The winner heads to the NIT Final Four in New York City on March 27.
"We have our eyes set on Madison Square Garden," Singler said. "We're excited to get up to Washington and then have a chance to play at Madison Square Garden."
The Ducks and Huskies split their season series 1-1, with Washington winning in Seattle 76-60 and Oregon winning in Eugene 82-57.
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"I want to play Oregon just because they beat us so bad at their place," said Washington guard C.J. Wilcox, one of several Huskies who referenced the Ducks after their win against Northwestern last Friday. "We have a chance to get them back and show that we're a better team."
They'll get Oregon coming off its highest-scoring game since beating UC Riverside 108-67 Dec. 28, 2002.
"The offense was great and we moved the ball and transitioned well, but that defensive effort won't get it done on the road," Oregon coach Dana Altman said.
Devyn Marble led the Hawkeyes (18-17) with 31 points and made all seven of his 3-point attempts. He shot 10 of 15 overall.
Aaron White also scored 22 for Iowa, Melsahn Basabe had 17 points and Bryce Cartwright had 12 points and 10 rebounds.
The Ducks trailed 31-16 with 10:44 to play in the first half but climbed back and a 9-2 run to end the half cut their deficit to 51-47 at the break.
Oregon took the lead for good on a 3-pointer by Joseph with 11:44 to play in the game that made it 71-68, and the Ducks pushed their lead to as much as 12 points, 97-85, with 5:29 to play.
"It shows the character of this team," Sim said. "We didn't get down on ourselves, we just clawed our way back. The veterans on this team kept everyone cool and we kept making plays for each other."
The Ducks shot 72 percent in the second half and made seven of their 11 3-point attempts after going 3 of 12 in the first half.
"Offensively, we couldn't play any better," Iowa coach Fran McCaffery said.
It was a much different story for the Hawkeyes, who appeared to be running away from the Ducks for much of the first half.
Leading the way was Marble, who had 19 points in the first half and made all five of his 3-point attempts. The sophomore forward came into the game just 15 of 48 on 3s this season.
The Hawkeyes made 8-of-12 3-pointers in the first half and their 51 points was a season-high allowed for Oregon.
Oregon didn't make its first 3-pointer until the 10:22 mark of the first half when Joseph made the Ducks first attempt in seven tries.
Led by reserve forwards Ashaolu and Emory, Oregon's bench outscored Iowa's reserves 43-17, and the Ducks also recorded a season-high 26 assists on 35 made field goals. Joseph led the way with a career-high eight assists.