Brian Anderson pounded four hits, scored four times and drove in three runs to help the Hogs score in every frame for the first time since a 32-8 victory over Saint Louis in 2010.
The No. 14 Razorbacks (33-17, 16-9) will go for their seventh SEC series victory Sunday when senior lefty Randall Fant pitches on Senior Day.
The Vols (20-27, 7-17) broke through for their lone run in the eighth against reliever Landon Simpson. Colin Poche got the final four outs for the Hogs.
Stanek (7-2) allowed five hits in seven scoreless innings. He sat down after 112 pitches. He was wild with his fast ball early, but the Vols could not touch his breaking pitches.
Stanek, with nine strikeouts, was settling in at the end with his fast ball finally hitting his spots, but UA coach Dave Van Horn elected to get two freshmen some work. Poche had not pitched in over one month. He recorded three strikeouts.
"We played extremely well," Van Horn said. "We got the leadoff man in six or seven innings. We had a chance to break it open early, but left the bases loaded when we scored only one.
"Stanek pitched well. His best innings were his last two when he finally commanded his fast ball. His breaking ball was good all night."
Tennessee coach Dave Serrano knew the Vols missed some chances against the 6-4 righthander in the first four innings.
"We weren't good offensively," Serrano said. "Obviously, Stanek is a really good pitcher, all American-type stuff, first round draft type stuff.
"But I thought early on he gave us a chance and we didn't take advantage of it."
The Hogs scored single runs in each of the first three innings, then broke it open in the fourth with Anderson's two-run homer to straight away center.
Joe Serrano led off the first with a double, scoring on Dominic Ficociello's single to center. Brett McAfee tripled and scored on a wild pitch in the second. Anderson led off the third with a single and would eventually score on Tyler Spoon's deep sacrifice fly.
In the fifth, Spoon doubled to right center and eventually scored on a Jordan Farris sacrifice fly. Anderson tripled home Matt Vinson in the sixth, then scored on Spoon's sacrifice fly.
The Hogs got another run on a sacrifice lfy in the seventh. Jake Wise walked, moved up on Mahan's single and moved to third on a Farris fly and scored on McAfee's fly.
Anderson led off the eighth with a single, drawing a standing ovation from the crowd for his fourth hit. A double would have given him the cycle. Two misplays by the third baseman would give the Hogs two more runs.
Anderson said he didn't think of trying for the double -- it was a clean single just to the right of the left fielder -- on the play.
"I didn't want to show up the other team," he said. "I was seeing the ball well and my hits found the gaps tonight."
The Vols could not find any pitching a day after Zack Godley went the distance. Serrano said starter Nick Williams didn't have anything working.
"It just wasn't Nick Williams' night," Serrano said. "His pitch count went up real high and he didn't have command of his breaking ball or fastball and made it very difficult. He kept us in the game at 3-0.
"We were still in the game and we went to the bullpen and we didn't have anyone who wanted to step up in this atmosphere. To me, this is a great atmosphere to pitch in and we didn't have that mentality tonight and that's why we got hurt in the end.
"Stanek made some big pitches when he had to. He had a good slider. His fastball command was marginal early, but he had a good slider and our guys weren't seeing it. Tip your hat to him. He threw a quality game and we didn't have a quality game."
It was another case of Stanek coming to the rescue after a Friday night loss.
"He's done a good job after a few of those Friday night games," Van Horn said. "We've lost some heartbreakers, although last night wasn't. Obviously, we knew Stanek was going. He's done a great job.
"I thought we were like two different teams. We were ready to play."
Stanek said, "I just think we have as good a chance to win as they do."
Van Horn said it was "one of our better games on paper. We were on top of our game."
The coach thought it was just a case of better focus.
"There were a lot of things going on this week," he said. "We had finals, there was graduation for some of the guys today. They whipped us last night and Godley was very good. But we were more focused tonight."