The Orangemen held the Tigers to just 38 percent from the field and forced 20 turnovers, to win their 11th straight game.
Carmelo Anthony had a quiet 16 points, but also added 11 rebounds. Freshman Gerry McNamara added 14 points and seven assists, while fellow starters Kueth Duany had 10 and Craig Forth 11.
"Having all five starters in double figures is what this team is all about," McNamara told Suathletics.Com. "It isn't just one or two guys."
Ricky Clemons finished with 26 points and dished out seven assists, but the bigger story was Arthur Johnson.
The center, who had a string of three straight double-double games, finished with 17 points and 11 rebounds, but was a non-factor against a Syracuse zone that had had trouble matching up with previous centers.
Syracuse took a 61-48 lead with just under 11 minutes in the second half before Missouri nailed some key shots on a 9-0 in two minutes.
The Orangemen went on a 10-0 run of their own, keyed by a three by McNamara. The guard would add another three on the run, followed by Anthony, to make is 71-57 with six minutes left.
"That was it," Syracuse coach Jim Boeheim said to Suathletics.Com about the threes. "Those were the key plays."
Free throw shooting was suspect for the Orange. Combined, the team went 11-for-22, with Warrick going just 4-for-11.
No. 25 Syracuse upsets No. 13 Mizz
Cuse Nation Top Stories
Jim Boeheim Previews 2016-17 SeasonSyracuse head coach Jim Boeheim looks ahead to the 2016-17 season and discusses a variety of other topics.
Cuse Nation6:00 AM
Quentin Hillsman Previews 2016-17 SeasonSyracuse women's basketball head coach Quentin Hillsman previews the upcoming season.
Cuse Nation4:55 AM
Orange Madness RecapSyracuse had their Orange Madness event Friday night to kick off the basketball season.
Cuse Nation4:15 AM
Matchup Preview: Syracuse at Boston CollegeFull matchup preview, breakdown and analysis for Saturday's game between Syracuse and Boston College.
Cuse NationThursday at 8:45 PM