Iroegbu led the Cougars with 20 points and added six rebounds and four assists.
"Ike is going to be really good," teammate DaVonte Lacy said. "This was his third game. Coming into 13th-ranked Gonzaga, he showed what he could do."
Iroegbu wasn't too impressed with his own numbers, though.
"I don't really think about stats when I'm playing," he said. "I'm just trying to help my team win."
Kevin Pangos scored 27 points and Drew Barham added 17 for the Zags. David Stockton had nine assists and Barham grabbed eight rebounds.
"It was a tough game with a local team that wants a piece of us real bad," Gonzaga coach Mark Few said. "Our guys played with fire."
Pangos shot 8 of 13 from the field, including 5 of 8 on 3-pointers, as Gonzaga (4-0) scored at least 90 points for the third time this season.
"Kevin was aggressive," Few said.
The guard is one of 50 players on the Naismith Trophy Watch List.
Few also praised Gary Bell Jr., who had 12 points despite early foul trouble, and noted that Stockton scored nine to go with all those assists and didn't commit a turnover.
"That's like his old man's numbers," Few said, referring to Hall of Fame guard John Stockton, a Gonzaga product.
Few also liked the play of center Przemek Karnowski, who had 12 points, six rebounds and two blocked shots.
"He was a presence in there," Few said.
Lacy had 14 points for cold-shooting Washington State (2-1).
"We just don't have the experience right now to compete with a team at the level of Gonzaga," Washington State coach Ken Bone said. "They were by far the better team."
Washington State was held to 44 percent shooting by Gonzaga, which shot 55 percent. The Bulldogs had 20 assists and outrebounded the Cougars 35-30.
Gonzaga scored the first basket of the game and never trailed. The Bulldogs made six of their first eight shots to take a 16-6 lead, capping the run on a 3-pointer by Barham.
"We wanted to get out and be really aggressive from the start," Barham said.
Jordan Railey's basket brought WSU to 24-18, but Barham's third 3-pointer extended the lead to 29-20.
Sam Dower Jr. completed a three-point play and Bell sank a long 3 as Gonzaga pushed its advantage to 37-25. Pangos' 3-pointer a minute later made it 40-26.
Washington State put together a 7-2 run that started when Iroegbu was fouled and sank all three free throws. The Cougars pulled to 43-33 with 3:39 left in the first, but Pangos answered with a pair of 3s and Washington State was scoreless the rest of the half, allowing the Zags to go into halftime ahead 49-33.
Washington State shot just 35 percent in the first half, including 3 of 13 from 3-point range. Gonzaga was at 55 percent, including 8 of 14 on 3-pointers. Pangos scored 20 points in the opening 20 minutes, while Iroegbu had 15.
"We think he has a chance to be a special player," Bone said of Iroegbu.
Karnowski opened the second half by completing a three-point play for Gonzaga to push the lead to 52-33.
But the Cougars were not done. Lacy, Dexter Kernich-Drew and D.J. Shelton all sank 3-pointers to pull WSU to 54-42 early in the second. A layup by Royce Woolridge cut Gonzaga's lead to 57-48 with 15 minutes left.
Gonzaga replied with a 13-4 run, including a pair of 3s by Barham, to rebuild the lead to 70-52.
Unanswered baskets by Barham, Kyle Dranginis and Stockton pushed Gonzaga's advantage to 77-54 with 10:08 left, and the Cougars did not threaten again.
Gonzaga edged Washington State 71-69 last season, but the Cougars lead the series 98-50.
Gonzaga is 124-8 in the McCarthey Athletic Center since it opened in 2004.