Jefferson followed with back-to-back baskets before being injured and the Jazz held on to beat the Magic, who missed their final four shots.
The Jazz built a 24-15 lead in the first quarter.
Jefferson scored six points and Mo Williams added five in the quarter as Utah dominated. The Magic committed six turnovers and shot only 7-for-19 from the field.
Orlando got as close as 28-23 early in the second quarter on a basket by rookie Andrew Nicholson.
The Jazz quickly countered, however.
Gordon Hayward made two free throws and Paul Millsap scored seven points in a span of 85 seconds. When Marvin Williams found himself mismatched against Magic point guard Jameer Nelson, he went inside and scored.
Williams' layup capped an 11-4 run and gave Utah a 39-27 lead with 5:58 left.
By halftime, Millsap scored 16 points and Utah limited Orlando to 35.9 percent shooting as the Jazz ended up with a 45-34 lead. Aaron Afflalo led Orlando with 12 points, but no other Magic player managed more than six.
The Jazz still owned a 56-45 lead with 71/2 minutes left in the third quarter before they misfired on five straight possessions.
Orlando went on an 8-0 run and got as close as 56-53, but Utah converted six of its final nine possessions during a 12-4 flurry of its own to re-establish an 11-point lead going into the fourth quarter.