Brandon Knight contributed 21 points and six assists for the Bucks (6-21). Butler, who missed the previous 12 games with a swollen left knee, also had 11 rebounds.
Thaddeus Young had 30 points and 10 rebounds to lead Philadelphia. Spencer Hawes added 25 points and 11 rebounds.
Both teams were coming off overtime games Friday. The Bucks lost 114-111 at Cleveland, their fifth consecutive defeat, while the 76ers nipped the Brooklyn Nets 121-120 at home.
Milwaukee, owner of the league's worst record, led throughout most of the game and built a 19-point cushion early in the fourth quarter. The 76ers pulled within seven with about one minute remaining, but the Bucks converted 10 consecutive free throws to secure the win.
The injury-depleted Bucks played without starting center John Henson, who bruised his knee in a collision with the Cavalier's Anderson Varejao in the loss at Cleveland Friday night. Henson's absence left Middleton as the lone Milwaukee player to appear in all 27 games this season.
Rookie center Miroslav Raduljica had a season-high 14 points in Henson's absence.
After trailing by 10 at the half, the 76ers opened the third quarter with an 8-0 run. The Bucks regained control with a 15-4 run midway through the quarter and held an 85-72 heading into the fourth. Middleton led the Bucks with 10 points in the quarter.
The Bucks held a double-digit lead for nearly the entire second quarter, growing their margin to as many as 15 with two minutes remaining. Milwaukee, bolstered by 51 percent shooting over the first two quarters, held a 59-49 lead at halftime. Knight had 17 first-half points, while Butler added 13 points and seven rebounds.
Young had 15 points and eight rebounds in the first half for Philadelphia, which shot just 40 percent.
The Bucks grabbed a 29-23 lead after the first quarter, paced by Middleton's seven points.
NOTES: Philadelphia has lost 12 consecutive road games. . Former MLB star and one-time Milwaukee Brewers executive Sal Bando visited Bucks' coach Larry Drew before the game. "Sal played in Kansas City, which is where I'm from. He was one of my heroes. I came up playing baseball. It was my passion. Basketball was secondary," Drew said. .The Bucks used their 15th different starting lineup in 27 games this season.