Former Manchester United star Nani scored twice in the first half to help Orlando set up a showdown with Portland Timbers in Wednesday's (AEST) showpiece.
Minnesota's Mason Toye reduced the deficit with seven minutes remaining, but Benji Michel's 96th-minute effort sealed Orlando's progression in Florida.
Nani put Orlando ahead after 36 minutes at the Walt Disney World Resort, where the Euro 2016, four-time Premier League and 2008 Champions League winner broke the deadlock.
Robin Jansson played a ball over the top to Nani, who controlled brilliantly before poking the ball past Minnesota goalkeeper Tyler Miller on Friday (AEST).
Nani then produced a moment of magic to double the lead six minutes later, the Portugal winger collecting the ball on the edge of the area, drifting onto his right foot and curling a shot past Miller.
Minnesota's first shot on goal did not come until the 75th minute – Raheem Edwards' free-kick forcing Pedro Gallese into a fine save.
Kevin Molino supplied his third assist to Toye as Minnesota kept their hopes alive with time running out, however, substitute Michel struck in the sixth minute of stoppage time to put the result beyond doubt.