Mike McCall had 18 points and Kwamain Mitchell scored 10 of his 12 in the second half to help the Billikens rally for a 65-61 win over the No. 15 Bulldogs on Friday night.
"I said it all week ... that's a heck of a basketball team," Stevens said.
The Billikens denied Stevens the opportunity to move within one victory of tying for the most wins in an NCAA coach's first six seasons. Stevens is 161-46, tying him with North Carolina State's Everett Case. Pittsburgh's Jamie Dixon was 163-45 in his first six seasons with the Panthers.
Dwayne Evans added 17 points for the Billikens, who won for the fourth time this season against a Top 25 opponent—a school record—and earned their ninth victory in a row in Atlantic 10 play. The previous eight had all been by 10 points or more.
Saint Louis (21-5, 10-2) remains firmly in control in the conference, holding a one-game lead over No. 24 Virginia Commonwealth. The Billikens beat VCU 76-62 on Tuesday.
"We focus on the first four minutes every game, and today we faced a little adversity in the first half," Evans said. "That was our first deficit in a while ... the guys responded well and we ended up making a huge run."
The win also gave Saint Louis a season sweep of Butler, which had 23 turnovers in a 75-58
"To lose to a team twice, it hurts more than most," said Butler's Roosevelt Jones.
Butler (22-6, 9-4) scored the game's first four points but needed Rotnei Clarke's 3-pointer 5:17 into the game to regain the lead at 10-9. Kellen Dunham then went on a personal 7-0 run for the Bulldogs, who led for the remainder of the first half and were ahead 34-29 at the break.
The Billikens took control to open the second half, scoring seven of the first nine points after halftime to take a 37-36 lead they would never relinquish. Mitchell's layup put Saint Louis back in front with 17:20 to play.
"I think the start to the second half was key," said Saint Louis coach Jim Crews.
Saint Louis didn't make it easy on itself with an 8-of-17 showing at the free throw line in the second half, which allowed Butler to stick around.
"Yeah, we got to work on that," Evans said. "We'll address that in practice."
Jones made a layup and was fouled with 5:26 remaining, but he missed the free throw and Saint Louis retained a 57-56 lead.
"In a game like this, every single point, every single play matters," said Stevens, who watched his Bulldogs also struggle at the line after the break with a 7-of-14 performance.
Evans made a layup after Jones' miss to extend the Saint Louis lead to 59-56. Jones hit two free throws to bring Butler within 59-58 with 3:32 to play, but with a chance to take the lead, Kameron Woods missed two free throws with 2:56 remaining.
Butler turned the ball over on a charge by Clarke and Mitchell hit two free throws after being fouled by Jones on the other end to put Saint Louis ahead 61-58 with 1:58 to go. Evans added a putback and Butler was forced to foul the rest of the way.
Dunham led Butler with 14 points, all in the first half. Clarke and Jones each scored 13 for the Bulldogs, who went 9 of 25 from the floor in the second half.