The Hawkeyes might not be able to afford to keep bringing him off the pine much longer.
Jarrod Uthoff had 15 for the Hawkeyes (11-4, 2-0), who prevailed thanks largely to a 31-13 edge on made free throws.
Twelve of those came from Olaseni, who added five rebounds, three crucial field goals and plenty of energy in just 22 minutes.
"We were determined to go inside and get to the free throw line. He's just playing with such confidence," Iowa coach Fran McCaffery said.
Nebraska's Shavon Shields led all scorers with 25 points. But the Cornhuskers (8-6, 0-2) had just two points in the final 2:43, and Iowa held Cornhuskers star Terran Petteway -- who fought through a shin bruise suffered early in the first half -- to just 11 points.
Iowa holds the rare distinction of two road wins over ranked opponents after winning at Ohio State last week.
The Huskers made the Hawkeyes work to earn their best league start since 2002-03.
Shields helped Nebraska take a one-point lead midway through the second half. Iowa rallied with an 11-3 run -- capped with a rare White 3 -- to move back in front 61-54 with 4:39 left.
The Hawkeyes were the aggressors early on, which allowed them to maintain a slim lead despite yet another stretch of cold shooting from the perimeter. Iowa got to the line 19 times in the first half and converted 15 times for a 35-28 lead.
Iowa's offense grew stagnant to start the second half though. Nebraska's did not, and the Huskers pulled ahead 51-50 with 8:09 left. Back-to-back 3s from Uthoff and Anthony Clemmons gave Iowa the lead back, and the Hawkeyes never gave it up.
"We were also getting stops, so it's a combination of both. We weren't trading baskets. We got a little bit of separation," McCaffery said. Nebraska finished with just five assists against 10 turnovers, and it committed 24 fouls.
"Play hard without fouling. That's what we're trained to do," Nebraska coach Tim Miles said. `I was just disappointed that we weren't able to play better defense."
Iowa: The Hawkeyes offered free hot chocolate to all of the fans that braved the weather to attend the game, as a snow storm ravaged Iowa Monday night and left the arena half-empty. Those who made it watched a team that could be on the verge of rejoining the Top 25. Iowa received 63 points in Monday's poll, which was second among teams who didn't get ranked.
Nebraska: The Huskers hit 10 of their first 18 shots, but they finished just 2 of 14 on 3s and 13 of 21 from the line.
White set a new school record with his 517th made free throw late in the first half. He broke the mark set by Iowa great Roy Marble from 1986-89. But that shooting form has rarely translated from 20 feet out. White is just 24 percent on 3s this season, which made his crucial 3 so promising for the Hawkeyes.QUOTE OF THE NIGHT
"I'm not going to divorce them when things are bad and marry them when things are good," Miles on Nebraska's 0-2 league start.
Iowa hosts Michigan State on Thursday.
Nebraska hosts Rutgers on Thursday.
***Posted by Josh Harvey