Danny Granger also had 19 points for Indiana, which trailed by nine points in the second half.
Jones, who played sparingly under former coach Jim O'Brien, keyed the victory by making six of seven shots from the field - including 2 of 2 from 3-point range - as Indiana rallied from a seven-point deficit to start the fourth quarter.
Kevin Love finished with 22 points to lead Minnesota, which entered having won its last two.
Josh McRoberts had 12 points and rookie Paul George had 11 points and four assists for Indiana, which moved into the final playoff spot in the Eastern Conference with a victory over Charlotte on Wednesday.
Backup A.J. Price scored eight points during a 10-3 run to start the fourth quarter for Indiana, which trailed by seven to start the period. Two free throws by Jones gave the Pacers their first lead of the second half, 95-94, with 9 minutes remaining, and Indiana did not trail again.
Mike Dunleavy scored 14 of the first 16 points for the Pacers, who led 18-9 early before the Timberwolves quickly cut into the lead and made it a tight game through halftime. Dunleavy shot 4 of 4 early, including 3 of 3 from 3-point range. He also had a 3-pointer negated because he stepped out of bounds.
Lazar Hayward had 12 points off the bench in the first half for Minnesota, which tied it late in the first quarter and made it a 58-56 lead at halftime.
Minnesota pushed its lead to 67-58 before Indiana stabilized and went on a 16-8 run. It stayed close until Jones got hot from inside and outside in the final period.
Tyler Hansbrough added 14 for Indiana, with 10 coming in the first half.
NOTES: Minnesota entered on its first two-game road winning streak since 2009 despite missing Michael Beasley, Darko Milicic and Luke Ridnour for the two victories. None of the three played Friday.