New Jersey came back from an 11-point deficit in the third period to turn the game into a tense battle but the Timberwolves made the plays down the stretch to win for the fourth time in six games.
Barea then made two foul shots with 18 seconds to play and, after Kris Humphries scored on a dunk for the Nets, Ridnour hit two more.
That gave Minnesota a three-point cushion and the Timberwolves held on for the win when Rubio stole the ball from Morrow to prevent New Jersey from getting off a potential tying long-range effort.
Minnesota won its third straight road game, something the team had not done since April 2009. Nikola Pekovic had 27 points and 12 boards off the bench to lead Minnesota while Kevin Love had 20 points along with 10 rebounds.
Morrow scored a career-high 42 points for New Jersey, which has dropped three out of four.