The goal was Arango's 12th in 14 matches since joining LAFC (11-12-8, 41 points) in early August. He has six in his past three matches.
Osvaldo Alonso scored his first goal of the season for Minnesota United (12-10-9, 45 points).
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LAFC was without 2019 MLS MVP Carlos Vela (quadriceps) for the 11th straight match.
Minnesota United held an 18-6 edge in shots and put seven on target to LAFC's four.
Goalkeeper Jamal Blackman made six saves as LAFC increased its unbeaten streak to four (2-0-2). The club entered the match in ninth place in the Western Conference and is trying to make a late move.
Goalkeeper Tyler Miller made three saves for Minnesota United, who are 2-0-1 over their last three games. The team was in sixth place entering the day.
Minnesota United knotted the score in the 65th minute when Alonso scored on a rebound.
Emanuel Reynoso lined up for a free kick and his left-footed blast was saved by Blackburn. But the rebound bounced directly to Alonso, who sent a right-footed shot into the net.
Minnesota United had a solid chance to take the lead in the 77th but Blackman made a lunging save on Franco Fragapane's right-footed shot.
Minnesota United dominated the flow in the first half but found themselves trailing at the break.
Arango did the honors for LAFC as he punched a free kick through the wall and it headed directly toward Miller.
But the ball slipped through Miller's hands and went right through his legs as Arango transitioned from feeling disappointment to expressing elation.
One of Minnesota's best first-half chances came in the fifth minute when Robin Lod broke in and received a pass to his left foot from Fragapane. But Lod sent the shot just wide of the left post.
LAFC had an opportunity to make it 2-0 in the ninth minute of first-half stoppage time. Brian Rodriguez delivered a cross to Arango but his close-range right-footed blast was saved by Miller.