Maze's 12-footer with 5.4 seconds left was the game-winner and gave Tennessee a 74-72 win over the University of Arkansas Wednesday night before a crowd of 15,055 at Bud Walton Arena.
Stefan Welsh and Michael Washington each had shot attempts before the game ended, but both were off to let the Vols (14-7, 5-2) sneak out with a win.
"This is a big step for us," Tennessee head coach Bruce Pearl said. "Beating Arkansas is significant. They knocked us out of first place last year. Two years ago they were our first road win. That game catupuled us and this win may do the same for us this year. These wins are the ones that make a team a championship team."
Welsh had a game-high 22 points, Courtney Fortson 19, Washington 18 points and 11 rebounds and Jason Henry 11 points for the Razorbacks (13-7, 1-6).
Arkansas played just seven players in the contest.
"If you look at the stats, we outrebounded them (32-30), scored more field goals (28 to 27), had the same number of threes (both 7 of 24), but just not as many free throws," noted Arkansas head coach John Pelphrey, whose team was 9-of-17 from the line to Tennessee's 13-of-18.
Welsh - who said he would have traded all 22 of his points for a win - said he felt his final shot was plenty good enough.
"It was a good look," Welsh said. "(Wayne) Chism did a good job of stepping up to contest it, but it was a good look, one I should make. I should have hit it.
"We got a second chance, too," Welsh said. "It's a shot Mike Washington hits nine times out of 10. He's usually going to hit that. It just wouldn't go down.
"Up until that, Courtney Fortson did a good job of drawing contact and making shots," Welsh added. "I came up the court and thought I could get a good look, though."
Fortson, who also had 6 assists, had hit a shot in the lane with 11 seconds left to tie it 72-72.
Before that Tennessee's Tyler Smith and Wayne Chism along with Arkansas' Fortson and Washington had traded baskets.
Chism's old-fashioned 3-point play capped seven straight points by the Vols to give them a 64-61 lead with 4:59 left in the game.
Fortson - who has been woeful from 3-point range and was 2 of his last 30 with a desperation bank shot earlier in the game included - then swished a 3-pointer to tie it 64-64 with 4:11 left in the clock.
His runner in the lane would give his team the lead, but buckets by Smith and Chism had Tennessee back up 68-66 with just over two minutes showing in the game.
"Fortson's a good player," Pearl said. "He's a nightmare to cover. I tried to keep him as far away from the basket as possible. At the end of the game, I would have done the same thing. I would have given the ball to Fortson instead. That's his shot."
There were then six straight baskets made to decide the game with Maze's the last make.
"It was huge for Bobby and his teammates," Pearl said. "It wasn't lucky, he just drove down and picked a good spot."
Chism had 22 points and 9 rebounds to lead Tennessee, Smith 16 points and Maze and J.P. Prince added 13 each.
"I think Tennessee is outstanding," Pelphrey said. "Their two front court guys are a great tandem, maybe the best in the league." Welsh had 13 of his points and Henry 9 of his in an opening half that was just a series of runs.
Tennessee jumped out to an 8-1 lead only to see Arkansas roar back with a 16-0 run that put the Razorbacks up 17-8 when Welsh scored inside with 9:18 left in the first half.
The Vols answerered with their own 12-0 spree, good enough for a 20-17 lead when Scotty Hopson soared through the air for a 360-degree slam.
Back came Arkansas with an 8-0 spurt with Welsh's 3-pointer getting them up 25-20 at the 5:17 mark.
It was fairly even from that point until intermission with Washington's lay-up with 1.7 seconds left sending the home team to the break with a 35-33 lead.
Tennessee scored the first nine points of the second half with Chism's 3-pointer surging the Vols ahead 42-35 with 17:06 left in the game.
Welsh jump-started his team with two free throws and then two straight steals resulting in buckets for Henry and himself to cut it to 42-41 at the 15:44 mark.
Fortson's ridiculous 3-point bank shot from 30-feet away with 1 second on the shot clock tied it at 44-44.
With the game tied at 49-49, Welsh buried a 3-pointer and then Washington got loose inside with 10:12 left to put the Razorbacks up 54-49.
Tennessee shot 48.2 percent from the field to the home squad's 45.9.
Welsh said the game came down to not securing rebounds.
"We shouldn't have gotten down," Welsh said. "We could have done a better job of rebounding. It wasn't our bigs. We have to do a better job of team rebounding.
"Tennesee hit a difficult shot at the end. Give them credit."
Fortson was asked how it felt to make some tough shots.
"I wouldn't exactly call them tough," he said. "Those are shots that I work on after practice so I expect to make them. I work on them."
The Razorbacks will return to action Saturday afternoon when it travels to play at Mississippi State in a 2 p.m. game.
Welsh said the Hogs still think a run is left in them.
"We still believe we can play in March," Welsh said. "Times are tough right now. We should huddle up and handle this adversity. Good times have got to be coming."
Courtney Fortson pushes the ball up the court.
Fortson gets deep inside the Tennessee defense.
Fortson draws contact.
Arkansas fans let the Tennessee coaches have it.
Jason Henry fires from long range.
Henry puts in a follow shot.
Stefan Welsh fights in the paint.
Michael Sanchez puts up a shot.
Mike Washington puts home a layup.
Washington is free for a layup.
Photos by Marc F. Henning, Hawgs Illustrated