"It's awesome to win in a Red Bull at the Red Bull Ring", said Verstappen, who was supported by an "Orange army" of more than 20 000 fans.
The victory was the 20-year-old driver's first of the season, and fourth of his career.
At Ferrari, Sebastian Vettel has a contract until the end of 2020.
The German, whose team did not invoke team orders for Raikkonen to cede position as might have been expected, clawed back the overall lead by a single point from Mercedes rival Hamilton.
The double-retirement was a first for McLaren since the 2016 Spanish Grand Prix, which Verstappen won on his Red Bull debut after Hamilton collided with team-mate Nico Rosberg on the opening lap.
Vettel leads the title race with 146 points ahead of Hamilton on 145, Raikkonen on 101 and Ricciardo on 96.
With Mercedes winning the last four drivers' and constructors' championships, and trading the lead with Ferrari this year, Horner recognised the champions could have lured Ricciardo away.
Hamilton retired due to a loss of fuel pressure with eight laps to go as he was looking to regain his title lead following a Mercedes strategy blunder and tyre problems.
On a bleak outing for the champions, who had not been beaten at the Red Bull Ring since Austria returned to the calendar in 2014, Hamilton's teammate Valtteri Bottas retired with a mechanical failure.
The Finn had started from pole, his first of the season, but lost out to Hamilton at the start and dropped to fourth before fighting back to second. "My focus was always on the track but for the last few laps I could look a little bit to my left and they were really cheering me on, it was awesome".
Verstappen hit the front after Mercedes kept Hamilton out on track during a virtual safety auto period that followed Bottas's retirement, with the other contenders pitting for fresh tyres.
He was passed by Ricciardo for the place on lap nine, but a solid stint on the soft-compound tyre after his pit stop ensured he could capitalise on the misfortune around him and guarantee his fifth podium of the season.
Mercedes' chief strategist James Vowles came on the radio as the bearer of bad news, admitting his error as Hamilton struggled to comprehend what had happened.
"Hats off to him", said Horner.
Although the team has scored three opportunistic wins, it has also left plenty of points on the table.
Romain Grosjean was fourth ahead of his Ferrari-powered Haas teammate Kevin Magnussen, Esteban Ocon and his Force India teammate Sergio Perez.
Sauber recorded is first double-points-finish since 2015 thanks to Charles Leclerc and Marcus Ericsson's ninth and 10th places.