After drawing with Japan, Koeman was criticised in the Dutch media both for his side's slow attacking build-up and his ineffective defensive substitutions when leading.
From the first whistle in Houston it was clear he and his players wanted to send a message of intent, as orange shirts ran at bewildered Sweden defenders in wave after wave of breathless attack.
Koeman clearly wanted his side to be more direct - Brobbey gave them a central focal point they lacked against Japan as he helped both start and finish moves.
Sweden's back three were constantly dragged out of position by Brobbey's hold-up play and the movement of Malen just off him, allowing Dutch runners to exploit space down the flanks.
To their credit, Sweden improved upon adopting a back four after the first-half hydration break and finished the half the stronger side, but could not convert a flurry of half-chances.
Koeman responded to his critics once again at half-time with an inspired substitution.
Summerville played with the energy and desire of an attacker hoping to reclaim his place in the starting line-up - his clever pass set up Dumfries to assist the third goal, before he turned provider for Gakpo's second.
He can take huge credit for stopping the Sweden comeback before it gained steam, though a blow to the head he suffered late on could leave Koeman sweating.
For the second time this tournament the Netherlands XI did not feature a single Eredivisie player, while all four goalscorers in this match played in the English top-flight last season.
Bar a late first-half push, Sweden's own Premier League strikeforce of Alexander Isak and Viktor Gyokeres had quiet evenings.
Both were starved of service, but showed promising signs of link-up play. If their defensive and midfield colleagues do not up their game then Liverpool and Arsenal respectively can expect them to report for pre-season training bang on time.
That said, Hungary are the only side in World Cup history to win their opening game by four goals or more and fail to progress from the group stage after they beat El Salvador 10-1 in 1982.
As three-time runners-up, the Dutch are known as World Cup bridesmaids. After being written off by many, Koeman is determined to take his nation all the way.
Image source, Getty Images
