Hunou was playing in only his fourth MLS game after signing with the club in April.
Minnesota's last four goals have come from players who have joined the club mid-season, with the other two scored by Argentine forward Franco Fragapane.
Tyler Miller made two saves to keep his fourth clean sheet of the season as Minnesota won its second straight and extended its unbeaten run to six matches.
The result bumps Minnesota United into a tie for fifth with Houston in the crowded Western Conference standings, and ahead of Portland and Salt Lake by a point.
Steve Clark made four saves, including two exceptional stops in the second half, to keep the Timbers in the match.
Portland outshot Minnesota 22-12 with many of those chances coming after halftime. But a combination of six defensive blocks, narrow misses and poor finishing kept the home side from finding a late equalizer.
The teams completed nine minutes of second-half stoppage time, in part because of an extended stoppage after it appeared Portland's Diego Chara took issue with something said by an opponent, prompting a conference between referees and the team captains.
Before all that, Hunou put Minnesota in front in the second minute. Bebelo Reynoso spotted Fragapane with a throughball on the left side of the penalty area.
Fragapane cut a cross back toward the penalty spot and Hunou finished easily past Clark from about 10 yards.
Ten minutes after halftime, Clark sprawled to deny Hunou and Niko Hansen in quick succession with point-blank saves.
But the Timbers couldn't take advantage. Jeremy Ebobisse misfired on a wonderful cross from Eryk Williamson in the 63rd minute, Bill Tuiloma sent a header just wide in the 81st, and Miller might have just gotten a finger to push Claudio Bravo's long-range effort onto the right post in the 84th.