Messi opened the scoring with a trademark goal from the Argentine as the the 36-year-old curled home from the edge of the box after linking up with his former Barcelona teammate, Jordi Alba.
FC Dallas hit back with three quickfire goals to take control of a pulsating tie.
Goals from either side left Miami trailing 4-2 with 10 minutes remaining before an own goal and Messi’s sumptuous curling freekick from just outside the penalty area leveled the scores at 4-4.
The 2022 World Cup winner’s moment of magic forced a penalty shootout with a spot in the final eight on the line.
And Messi once again stepped up, calmly slotting home his penalty, while 18-year-old Benjamin Cremaschi converted his spot-kick to seal a 5-3 victory for Inter Miami.
The two-goal performance extends Messi’s good form since moving to Florida. He has now scored two goals in each of his last three games. Overall, he has scored seven goals in his first four games for the club.
“It is true that we count on the best player in the world,” said Inter Miami head coach Gerardo Martino “and you can’t ignore that.”
Inter Miami will host either Houston Dynamo or Charlotte FC at DRV PNK Stadium in the quarterfinals.
The Leagues Cup is joint competition organized by the top-tier soccer competitions in the US and Mexico which features every club in the top two leagues in North America.
The winner of the tournament qualifies directly to Concacaf Champions League round of 16.