Fans who had paid eye-watering ticket prices averaging more than $450 to see Messi play his first match in Salt Lake City were treated to a full 90 minutes from the Argentine.
Messi created several chances but couldn't get past Brazilian goalkeeper Rafael Cabral and had to rely on fellow Argentine Rodrigo De Paul to break the deadlock in the 82nd minute.
De Paul's blast following a corner eluded the grasp of Cabral and slipped into the top-right corner.
Second-half substitute Suarez sealed the victory a minute later when he latched on to German Berterame's header and found the net with a left-foot strike.
"I think we played a great first half," De Paul told Apple TV after Miami's second straight victory under interim coach Guillermo Hoyos.
"It was a beautiful goal, and as long as it helps the team, that's great," he added after helping to end Salt Lake's six-match unbeaten run.
Uruguayan Suarez, the 39-year-old former Liverpool and Barcelona attacker, got off the mark for 2026 with his 44th goal in 93 matches for Miami.
According to TickPick, Wednesday's match was the "most expensive MLS game of the season" with the average ticket price soaring to $468.
Messi's side are unbeaten since an opening-day 3-0 defeat to Son Heung-min's Los Angeles FC.
They remain second in the Eastern Conference with 18 points, one behind Nashville, who have a game in hand.
