Lionel Messi scored twice, including a brilliant late equaliser, as Inter Miami advanced past FC Dallas to the quarter-finals of the Leagues Cup on penalties after an enthralling 4-4 draw.

A trademark curling free-kick in the 85th minute, Messi's seventh goal in four games for Miami, took the game to a shootout after the Argentine's side had trailed 4-2 with 10 minutes to go.

Dallas exposed Miami's defensive weaknesses, in Messi's first game away from home, and kept Spanish midfielder Sergio Busquets relatively quiet for long stretches but the World Cup winner still made the difference.

"It's obvious that for him a free-kick around that area is like a penalty kick for another player," said Dallas's Spanish coach Nico Estevez of Messi's superb strike.

Dallas began brightly before Messi put Miami ahead in the sixth minute with a precise side-foot finish from a pull-back from Jordi Alba, the former Barcelona full-back who was making his first start for the club.

It was initially ruled out for offside but the decision was reversed after the referee, on review, ruled that Miami forward Josef Martinez had not blocked the view of the goalkeeper.

Dallas drew level in the 37th minute through Argentine Facundo Quignon, who swung home a cross from overlapping full-back Marco Farfan.

They went ahead on the stroke of half-time through Bernard Kamungo, who rounded Miami keeper Drake Callender.

Another Argentine, Alan Velasco, made it 3-1 in the 63rd minute with a free-kick from the left which flew untouched into the far corner.

Teenage substitute Benjamin Cremaschi took only a minute to reduce the deficit but an own goal from Robert Taylor restored the two-goal cushion for Dallas at 4-2.

Messi then chipped a free-kick into the box and Farfan, unchallenged, inexplicably headed into his own goal to keep Miami alive.

Five minutes from the end Messi strode up and slotted home a free-kick from 20 yards to take it to penalties.

The Leagues Cup, the tournament for clubs from Major League Soccer and Mexico's Liga MX, does not feature extra-time, with drawn games going directly to penalties.

Messi converted the first penalty in the shoot-out, Paxton Pomykal missed for Dallas and the 18-year-old Cremaschi secured Miami's place in the last eight with the final spot-kick.

"It's amazing what (Messi) can do," said Miami-born Cremaschi, whose parents are Argentine.

"He scored twice in almost every game and it's just impressive."

Miami were without a win in 11 games in Major League Soccer before Messi's arrival, but have triumphed in every game with him and Busquets in the team.

"You can see our mentality, how things have changed in this club, how we were willing to fight until the last second, especially with the quality players that we have," said Cremaschi.

"We know that we could be down by a bunch of goals and still come back in a matter of seconds."

Miami's Argentine coach Gerardo Martino said that Messi's magic and the result should not disguise the clear deficiencies in his team.

"Obviously being 4-2 down in the 80th minute and then coming back like that, we are very happy with the result.," he said.

"But the fact that we have gone through, shouldn't let us lose sight of the things that we have to improve."