Starting from second – and the dirty side – of the Hungaroring grid after missing out on pole to bitter rival Lewis Hamilton by just 0.003secs, Verstappen managed to get the crucial inside line on the run down to Turn 1.
Seven-time F1 champion Hamilton attempted to squeeze Verstappen out of the picture, and for a moment flashbacks of their past collisions appeared, but the Mercedes driver yielded marginally, giving the Dutchman enough of a view into the first corner.
Hamilton again attempted to fight back, with the duo almost touching wheels, but Verstappen managed to make his move stick, from which point there was no looking back as he coasted to victory by almost 34 seconds over McLaren's Lando Norris.
In taking the chequered flag, Red Bull has now set a new record of 12 consecutive victories, breaking a mark that has stood for 35 years when Ayrton Senna and Alain Prost led McLaren to 11 successive wins in 1988.
“We have achieved history, which is something very special for the whole team,” said Horner.
“To achieve the record of 12 consecutive grand prix victories, to break that record from 1988 – and I remember watching Ayrton Senna, Alain Prost, the great McLaren team at the time led by Ron Dennis, and to think it's taken 35 years, with the quality of the opposition we're racing against – is a phenomenal achievement, and something the whole team can be immensely proud of.”
What was remarkable in a season of considerable achievement for Red Bull was the margin of victory, particularly following a qualifying session in which the gaps were so fine.
There was no sense of the dominance to come, to which Horner remarked: “The consensus was that we'd put more focus into the higher temperatures (for the race) and the race pace as opposed to single-lap pace.
“Whilst Max was frustrated not to get the pole, he went into this race fully fired up.”
Horner has conceded, though, to a degree of nervousness in watching the start, adding: “A grid that has Lewis and Max starting alongside each other is always one as a team principal where you're thinking ‘I just hope I see the car out of the first turn'.
“But both drivers raced very hard, but fair. Max got a great start off the dirty side of the grid, and it was old school down to the first turn.
“Once he emerged out of that first turn, he really stamped his authority all over the race, controlling it from start to finish, and we had a phenomenal race car, converting that into a dominant one-three.”
With the season now at the halfway point, there is a real possibility Red Bull could achieve the perfect season and win every race.
A cautious Horner, however, added: “How long can we keep this winning run going? Who knows?
“We've got another challenge next weekend (Belgian Grand Prix), a sprint race, the variable conditions of Spa, and anything can happen, so we're really just taking it pretty much one event at a time.”