The streak matches Portland's best run since winning 12 in a row during the 2001-02 season, the team's second-longest stretch. Portland's longest streak was 16 games in the 1990-91 season.
Al Jefferson had 22 points for Minnesota, which has the league's worst record at 4-24. The Timberwolves fell to 1-14 on the road.
LaMarcus Aldridge had 21 points and eight rebounds for the Blazers. Jarrett Jack added 14 points and was among six Blazers in double figures.
Portland, the youngest team in the NBA, started its streak with a Dec. 3 victory at Memphis after going 5-12 to start the season. Nine of the team's 12 wins have come at the Rose Garden, where the Blazers are 14-3 overall.
Portland was coming off an 89-79 victory over the Seattle SuperSonics on Christmas. The Timberwolves were defeated 105-101 by Golden State on Wednesday night.
Portland led by as many a nine points early, but the Timberwolves went ahead briefly in the second quarter, when Antoine Walker's layup made it 31-30.
Jack put Portland back ahead 44-42 with a pair of free throws. That was the start of a 13-4 run to make it 55-46 at the half.
Roy, last season's Rookie of the Year who was averaging 23 points a game during the streak, had a pair of fouls but did not appear to be injured when he sat the entire second quarter. He returned to start the second half.