In the fourth minute, Reynoso scored his first goal of the game off a failed clearance, which Robin Lod collected and provided the assist.
Reynoso made it 2-0 in the 20th minute when he dribbled forward, switched the ball with his feet to clear some space and found the net with another long-distance shot.
Minnesota earned its first-ever win over the Galaxy after nine meetings. It took them only a few moments into the match to end a two-game scoreless streak.
The Galaxy (11-9-5, 38 points) are winless in six straight matches (0-3-3). They had 65 percent of the game's possession but managed just two shots on goal, while Minnesota United converted on all three of their shots on target.
Finlay got free up the field, and Fragapane found him with a long ball that Finlay deposited into the goal after outrunning the Galaxy defense. The 66th-minute goal was the midfielder's second of the season, and when the Minnesota native was subbed off in the 82nd minute, he received a roar from the home crowd.
Finlay was inches wide of making it 4-0 in the 71st minute, missing a wide-open shot from close range with no one marking him. But by then, Minnesota United was in control of the match.
Minnesota repeatedly had attacking players break free for long runs with the ball, with defensive breakdowns from the Galaxy. Adrien Hunou had a chance after he got free and stayed onside, but his shot went high and wide.