Dixon's unassisted, left-footed shot from just outside and left of the 18-yard box extended Houston's unbeaten streak to five matches and propelled the Dynamo (8-7-11) from fourth to second place in the Eastern Conference standings.
Dixon entered the game in the 81st minute for Colin Clark and scored his first professional goal in his ninth game of the season.
Bobby Boswell equalized for Houston (8-7-11) in the 70th minute just 10 minutes after Luis Gil gave Real Salt Lake a 2-1 lead when he headed a cross from Fabian Espindola past Houston goalkeeper Tally Hall (two saves).
Espindola scored in the 28th minute to give Real Salt Lake (10-7-6) a 1-0 lead, but Houston dominated the second half and tied the game on Brian Ching's team-leading fifth goal of the season in the 47th minute.
Real Salt Lake, now winless in eight all-time matches in Houston, has just one win in its last five games (1-3-1), and Espindola's first goal snapped a scoreless streak of 425 minutes away from home.
Ching had a golden opportunity to give the Dynamo their first lead of the game in the 86th minute, but his header on a pass from Brad Davis was swatted away by Salt Lake goalie Nick Rimando (seven saves).