Oranje boss Ronald Koeman sprang something of a surprise by selecting Brobbey ahead of Crysencio Summerville, a goalscorer in their opening 2-2 draw with Japan, but the decision was quickly vindicated as the Sunderland striker scored twice in the opening 17 minutes on Saturday.
After Sweden had a goal ruled out at the end of the first half, Liverpool ace Gakpo then hit two in the first 10 minutes of the second half, and although Anthony Elanga pulled one back for Graham Potter's Sweden just before the hour, substitute Summerville had the final say in the 90th minute.
"That first goal had everything you could want. It was a brilliant start to the match. That gives you confidence," Dutch coach Ronald Koeman said after his side had been watched in Texas by the king and queen of the Netherlands.
Only five minutes in, Brobbey laid the ball off to Tijjani Reijnders, who swept it left for Gakpo to send in a low cross for Brobbey to poke in, and the second goal was almost a mirror image as Denzel Dumfries crossed low from the right and Brobbey again prodded home.
Sweden, who crushed Tunisia 5-1 in their opener, came to life after the first hydration break and thought they had a goal back late in the half but Gustaf Lagerbielke was one of several of their players who were offside as he bravely headed in Benjamin Nygren's free-kick.
Instead, Gakpo was able to kill off Sweden early in the second half. When Summerville, on for Donyell Malen at the break, sent in a low cross Brobbey could not quite stretch far enough to get his hat-trick, but Gakpo was left with an easy finish at the back post.
Eight minutes later, the Netherlands punished a mistake from Alexander Isak with a rapid counter as Summerville laid the ball off for Gakpo to cut in from the left and fire home.
Just before the hour Elanga gave Sweden something to cheer as he ran on to a through ball from Isak and clipped it beyond Bart Verbruggen, but Summerville sparked fresh Dutch celebrations in the 90th minute as he swept home from the edge of the box.
Potter's team will now have to do the job against Japan on Thursday to guarantee progression.Â
"Obviously really disappointed," the Englishman said. "It was a tricky one to analyse, we did lots of good things. We attacked, had good opportunities but you can't concede that many and hope to win."
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