The Red Bull driver battled from last on the grid and negotiated late rain to finish behind title rival Lewis Hamilton on the podium
The Dutchman started at the back of the grid in Sochi after Red Bull decided to change his engine and had worked his way through the field into seventh heading into the closing stages.
But the arrival of late rain presented Verstappen with the opportunity to change into intermediate tyres before the cars in front of him and the 23-year-old surged into second place to finish behind title rival Lewis Hamilton.
The Mercedes driver still reclaimed the lead in the title race with his 100th win in Formula One but Hamilton was left to credit Verstappen for “mega damage limitation” after the gap was reduced to two points.
“Today was like a victory for us,” Horner said to Sky, while also admitting that Red Bull had outlined a fifth-place finish as the best-case scenario before the race.
“To come from 20th on the grid to second, I think if anybody had offered us that we would have bitten your arm off.
“Max got the call right to go on the inters and it worked out well for him. The rain the last five laps came at the right time.”
Horner is predicting that the title race will go down to the wire with seven races to go this season.
The Red Bull boss said remaining two points behind Hamilton after the engine change left his team in a strong position ahead of the run-in.
“To come away from two Mercedes strongholds with only a two-point deficit in the drivers’ championship is hugely encouraging," il ajouta.
“I don’t think there’s any circuit that stands out as strongly as Russia and Monza [for Mercedes]. You could say it’s 50-50 in what’s left on the table.”