When Van Gaal retires, winning the International Champions Cup will not rank among his greatest achievements.
The Dutchman already has 16 winner's medals of greater prestige, but the importance of winning this money-spinning pre-season tournament cannot be discounted.
"This will give us momentum, for sure," the United manager said. "It's always better to win. First we beat Roma, then we beat Inter Milan with penalties but we were much better, then we beat Madrid and then we had a test against a Premier League team."
Sterling continued to cause United problems, and he should have had a penalty when Ander Herrera pulled him down in the box just before half-time.
Two minutes later, Mata's shot flew past Mignolet via a deflection off Mamadou Sakho.
And in the dying minutes Lingard put the result beyond doubt when he converted Ashley Young's cross.
Afterwards Van Gaal singled out Rooney, who was named player of the tournament for scoring three goals, for praise.
"He was always a man who is a winner," Van Gaal said. "He deserved (to be player of the tournament) because he scored a lot of goals and gave a lot of assists.
"The goal was very important for him. It was a wonderful goal when you see the attack and what he did to push the ball under the legs of the opponent but also in the corner of the goal. It was a great cross from Chicharito (Hernandez) also. It was a very good attack."
Rooney captained United for the first time on the tour, which took United to Los Angeles, Denver, Washington DC, Detroit and finally to Florida.
Darren Fletcher was named skipper in the other two International Champions Cup games while Tom Cleverley was given the honour of captaining the side in the 7-0 win over the Los Angeles Galaxy.
Van Gaal has to decide who will captain United next season, but he was giving little away on whether it would be Rooney.
"I'm always looking for opportunities to give players the captain's brace [armband]," said Van Gaal, who is thought to be considering Robin van Persie and Jonny Evan as serious candidates too.
"Today Rooney played for the first time 90 minutes. Fletcher has already done it two times, therefore he was the captain. Cleverley also played 90 minutes. I think you have to choose when it is possible in English style. But it has to be possible."
Liverpool manager Brendan Rodgers was disappointed to lose after taking the lead in Miami.
"We were well worth the lead," said Rodgers, whose team had beaten Olympiacos, AC Milan and Manchester City before arriving in the Sunshine State. "It looked like we should have had another penalty (when Herrera fouled Sterling).
"We conceded a disappointing goal and then conceded a second. But I am delighted with the whole tournament. We have been away what seems like a long time but we have worked hard and we have taken a lot of positives from this tour."
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