The Jazz led by 15 points with 7 minutes left by almost blew the contest when the Timberwolves staged a furious rally down the stretch, pulling to within 93-91 with 19 seconds remaining.
But Randy Foye sank four free throws in the closing seconds to ice Utah's first win four games.
Milsap grabbed eight rebounds, Jefferson added 11 boards and DeMarre Carroll chipped in with 11 points for the Jazz.
Minnesota was led by Ricky Rubio with 18 points, nine rebounds and 10 assists.
Derrick Williams (24 points, 16 rebounds) and Nikola Pekovic (19, 13) also had big nights for the T-Wolves.