Washington (48-12) advances to the College World Series to be held June 1-7 in Oklahoma City. Utah (37-16), hoping for its first World Series berth since a fifth-place finish in 1994, lost in the Super Regional for the second consecutive year.
"Losing's always frustrating," said Hogue, who played on the 1994 World Series team. "But, this team, you can't be mad at them. You can't be frustrated with them for more than two seconds because they did what they were supposed to do. They put it out there and went after it."
The 16th-ranked Utes, who forced the third game with a 9-8 victory on Saturday after dropping the series opener, simply could not get the big hit behind Katie Donovan (18-10), who allowed two runs on just three hits, striking out two and walking three.
"Something I knew I needed to get better at today was going right at them," Donovan said. "I figured it out after a couple innings and I went right at them. My defense made some awesome plays behind me and it worked."
Washington ace Taran Alvelo (32-7), who won the series opener, but took the loss in the second game, scattered eight singles and got key outs with runners aboard.
Utah, which allowed single runs in the first and second, cut the lead to 2-1 in the fifth, but the Huskies prevented a big inning with two outstanding defensive plays.
Delilah Pacheco led off with a single to left and BreOnna Castaneda followed with grounder up the middle, but second baseman Sis Bates made a sensational diving stop and flipped to second in time for the force out.
Alyssa Barrera followed with a double to the gap in left-center and Hannah Flippen was walked intentionally to load the bases with one out.
Trystan Melhart then made a diving grab of Urtez's looping liner in shallow right, but Castaneda came home on the sacrifice fly. Bridget Castro grounded out to second to end the inning.
Washington, which pounded five homers in the first two games, pushed across a pair of early small-ball runs.
The Huskies manufactured a run in the first. Ali Aguilar singled to open and Bates walked. Aguilar advanced to third on a fielder's choice force-out and scored on a wild pitch.
Washington made it 2-0 in the second. Melhart walked and Kirstyn Thomas singled. Both runners advanced on Kelly Burdick's sacrifice bunt and Aguilar followed with a sacrifice fly to right.
The Utes failed to capitalize on several scoring chances.
Utah threatened in the second when Urtez singled and Castro walked, but Alvelo struck out the next three hitters.
In the fourth, Flippen and Urtez opened with consecutive singles. Heather Bowen reached on a two-out infield single off Alvelo's glove to load the bases, but Kay Kay Fronden grounded out to second to end the inning.
In the sixth, the Utes had runners on first and second with one out, but pinch-runner Ryley Ball was thrown out attempting to steal third and Pacheco's blooper to third ended the threat.
"I couldn't be more proud of this team that I coached today," Hogue said. "They worked their guts out to be prepared to compete at the highest level. And, they came out and put it all out there today. I'm super proud of them."
• Utah outhits Washington 8-3, but strands eight runners.
• Katie Donovan, who got the victory in the second game, allows just two runs on three hits, but gets little support.