Philadelphia, who made the MLS Cup final last year and have a dominant record at home, were poised to be Miami's biggest test since the latter added the Argentinean striker to their roster last month.
But the visiting Miami once again got off to a quick start when a running Josef Martinez scored three minutes into the game on a pass from Serhiy Kryvtsov.
Messi was somehow left unguarded just past midfield where he caught a pass from Martinez and dribbled forward before firing a shot from distance in the 20th minute that rolled past Union goalkeeper Andre Blake, who was slow to react.
Jordi Alba further demoralized the Union with a goal just before halftime for a 3-0 lead as fans booed the home team as they headed into the locker room.
Philadelphia got one back through Alejandro Bedoya in the 73rd minute but David Ruiz found the net in the 84th minute for Miami, who have scored 21 goals in their last six matches.
Miami will face either CF Monterrey or Nashville SC, who play later on Tuesday, in Saturday's Leagues Cup final, Miami's first final appearance in club history.
The win also mean Miami will play in their first ever CONCACAF Champions League next year.
