The big win in front of nearly 69,000 put the delighted Dutch on the cusp of the knockout rounds and gave them liftoff after being held by Japan.
Despite the sobering loss the Swedes had plenty of chances but were denied by good goalkeeping and wasteful finishing.
They are still in with a good chance of progressing into the last 32.
Japan and Tunisia play later on Saturday in Monterrey, Mexico.
Sunderland striker Brobbey got his first start of the tournament and repaid Koeman with predatory goals after five and 17 minutes.
Before that the 24-year-old had scored only once for his country since making his debut three years ago.
In a game full of top Premier League talent, Liverpool’s Gakpo — who set Brobbey up for the opener — scored twice early in the second half.
Substitute Anthony Elanga pulled one back for Sweden just before the hour with a classy finish.
Crysencio Summerville had the last word for the five-star Dutch.
Two crew members from the historic Artemis II lunar mission were among the VIP guests, a nod to Houston’s place as the home of space flight.
The Dutch, twice pegged back in a lively 2-2 draw with Japan to start their title bid, made the brighter start in front of their orange-clad fans and King Willem-Alexander.
Brobbey, who came in for Summerville despite the winger scoring against Japan, started and finished the first goal.
It was made in the Premier League, with goalkeeper Bart Verbruggen, midfielder Tijjani Reijnders and Gakpo all involved.
Brobbey exchanged passes with Gakpo, before the Anfield attacker crossed in low from the left for his team-mate to stab in from close range.
Sweden, who thrashed Tunisia 5-1 in their first game, could not handle Brobbey’s muscular presence.
Up front the much-vaunted attack of Liverpool’s Alexander Isak and Viktor Gyokeres of Arsenal were feeding on scraps for Sweden.
Twelve minutes after his opener Brobbey made it 2-0 when a deflected Denzel Dumfries cross from the right fell perfectly into his path and he toe-poked past Kristoffer Nordfeldt.
Sweden’s English coach Graham Potter was in deep discussions with his backroom staff as the game threatened to run away from them.
At the unpopular hydration break Potter made a beeline for left-sided defender Gabriel Gudmundsson of Leeds United, who was being overrun by the flying Dumfries and Donyell Malen.
Sweden then had their best chance, Gyokeres crossing for an unmarked Yasin Ayari who completely miscontrolled the ball with his chest.
Gyokeres was next to fluff a good chance, failing to make proper contact after being played in by the largely anonymous Isak.
Gyokeres and Ayari twice both had further sights of goal, only to be denied by the increasingly overworked Verbruggen.
The Netherlands were hanging on by end of the half.
Koeman sent on Summerville for Malen at the break, and two minutes later it was mission impossible for Sweden, Gakpo prodding in from close range after yet another dangerous low cross from Dumfries.
All three goals were strikingly similar.
Gakpo scored a lovely fourth on 54 minutes, turning inside his defender before firing low into the bottom corner.
Nottingham Forest winger Elanga pulled one back five minutes later when he raced clear of the Dutch defence and rattled the ball past Verbruggen.
West Ham’s Summerville made it five in the dying minutes with his second goal in North America.
Sweden face Japan next while the Netherlands play Tunisia. (AFP)