Alberth Elis notched a pair of assists and Marko Maric made four saves for the Dynamo (2-2-4, 10 points), who followed up a 5-2 victory over Sporting Kansas City on Aug. 25 with their second win of the season.
Houston has won four straight meetings between the teams at home, including the last three without conceding a goal. The Dynamo posted a 2-0 victory over Minnesota United last September on first-half goals by Mauro Manotas and Christian Ramirez.
Greg Ranjitsingh finished with eight saves for Minnesota United (3-3-2, 11 points), who have lost three in a row since the conclusion of the MLS is Back Tournament.
Quintero made his presence known in the 28th minute of his first match against his former team since being traded from Minnesota in November. The 32-year-old accepted a sliding feed from Memo Rodriguez and unleashed a right-footed shot from the right side of the box that sailed into the corner of the net to open the scoring.
The goal was the club-best fourth of the season and third in two matches for Quintero, who recorded 21 goals and 20 assists in 57 MLS matches with the Loons in 2018-19.
Lassiter replaced Christian Ramirez in the 55th minute and doubled the Dynamo's advantage 10 minutes later after converting Elis' cross. The 25-year-old wasn't done, as he sent a left-footed shot from the top of the box inside the left post to give Houston to a 3-0 lead in the 70th minute.
Lassiter was signed by the Dynamo last month, with $50,000 in general allocation money heading to the Los Angeles Galaxy to complete the deal.