Marquette (25-5) did not miss a shot in overtime and reached the regional semifinals for the first time in nine years. It will next meet the winner of Friday's game between Pittsburgh and Indiana. The Midwest regional semifinals and final will be held in Minneapolis.
Missouri (22-11), which reached the West Region final as a 12th seed last year, closed the second half with a 12-4 run to tie the game at 80-80.
But Marquette was perfect in the overtime, hitting three of three from two-point range and three of three from beyond the arc. The Golden Eagles also made all six of their free-throw attempts in the extra session for a total of 21 points.
"I've never seen a team play as well as we did in overtime," Marquette Coach Tom Crean said. "I thought our execution on the offensive end couldn't have gotten any better."
"I have never witnessed a team shoot 100 percent in overtime," Missouri Coach Quin Snyder said.
Novak accounted for all three three-pointers, getting it started with a jumper from the left corner 22 seconds into the overtime.
After freshman Jimmy McKinney responded with a three-pointer for Missouri, Novak struck again with 3:54 left to give Marquette the lead for good at 86-83. Novak's third three-pointer of the overtime with 2:02 remaining increased the advantage to 93-89.
"Going into overtime, I came in and they called a couple of plays for me," said Novak. "At our shootaround yesterday the coaches ran a drill of what we call last-second shots and it paid off. I was able to knock them down today."
Novak's third three-pointer of the extra period ignited an 11-0 run.
"We put a hand in his face but he (Novak) was able to make the big shots," Snyder said.
Scott Merritt converted a layup inside with 1:01 left before Travis Diener made four free throws and Dwyane Wade added a pair in the final 47 seconds to open the lead to 101-89.
Marquette shot 57 percent from the field for the game, made 12 of 18 three-pointers and was 19 of 20 from the line.
"It is tough to play a team that shoots 66 percent from the three and gets 20 points from the line," Snyder said.
Rickey Paulding led Missouri with a career-high 36 points, including nine of 15 from three-point range.
Paulding had a chance to win the game at the end of regulation, but lofted a shot from the top of the key that fell short.
"I grabbed the rebound and I wanted to push the ball up the court as quick as I could," Paulding said. "I had a good look, it just came up short."
Arthur Johnson provided power inside with 28 points and a season-high 18 rebounds, but three of Missouri's starters -- Ricky Clemons, Travon Bryant and McKinney combined to shoot four of 27 from the field. Clemons, the Tigers' second-leading scorer at 15.7 points, had just five. He made two of 15 from the field, including one of 10 from three-point range. Bryant missed all six of his shots and went scoreless in 27 minutes.
"Shots just did not go down for them (Clemons, McKinney and Bryant) today," Johnson said. "It wasn't frustrating because all year they have knocked down those shots. Today they were just off."
Wade, the Conference USA Player of the Year with a 21.7 scoring average, played a superb all-around game with 24 points, eight rebounds and seven assists and received plenty of help from his teammates.
Diener, the sophomore point guard who missed practice time before the NCAA Tournament due to shin splints, was again a major force with 24 points. He made eight of 12 from the field.
He had a career-high 29 points, including five three-pointers, in the 72-68 win over Holy Cross in the first round.
Merritt had 18 points, including a layup and a dunk in overtime, and seven rebounds and Novak finished with a "perfect" 14 points in 17 minutes off the bench. He was four of four from beyond the arc and two of two from the line.
"When you have guys like Steve who can come in off the bench and hit big shots, that's a big lift," Wade said.
The Golden Eagles last reached the Sweet 16 in 1994, losing to Duke in the regional semifinals.