Before the game, the Union unveiled a banner celebrating their Supporters' Shield from last season.
Unlike last season, when the Union went unbeaten at home in nine games, they couldn't hold a lead this time around.
In the 27th minute, Sergio Santos had the Union's first solid scoring chance, but couldn't get a clean shot off in the box.
The scoreless first half was choppy in a physical game with numerous whistles and stoppages.
It was the third consecutive half without a goal for the Union, who opened the season with a scoreless draw last Sunday at Columbus Crew SC.
The Union nearly scored in the 50th minute when Kacper Przybylko had his left-footed shot deflected out of bounds for a corner kick.
Inter Miami countered in the 53rd minute, and Jay Chapman sprinted into the box wasn't able to control the ball.
Then in the 54th minute, Monteiro received a crisp pass from Przybylko and sent a shot past goalkeeper John McCarthy for a 1-0 lead.
Philadelphia's Cory Burke, who entered the game seconds earlier as a substitute, headed a ball just wide of the net in the 62nd minute.
In the 73rd minute, Federico Higuain took a free kick from about 25 yards out, and Gonzalo Higuain headed the pass into the net to tie the game at 1.
Inter Miami took a 2-1 lead in the 83rdminute when Federico Higuain headed home a cross in the box for his 58th career goal.
The Union earned a corner kick in the 88th minute, but the pass was quickly cleared out of the box.
Despite four minutes of stoppage time, the Union weren't able to equalize.