Hamilton was battling with Ferrari’s Sebastian Vettel for the Drivers’ Championship at the time.
In a crunch race in Budapest, Hamilton asked to pass Bottas in third place in order to chase the Ferraris.
The Finn agreed to let his team-mate through, in order to try and overtake Vettel and Kimi Raikkonen.
But after failing to reach the Ferraris Hamilton let Bottas back through and take the podium.
And Wolff says the respect between the two drivers proved to him Mercedes would take both drivers’ and constructors’ titles come November.
“For me the key moment was Budapest where we changed the drivers at the end of the race,” Wolff told the BBC.
“We stuck to our values.
“Lewis asked to give it a go and try and take over the Ferraris – and if it doesn’t work I will give Valtteri the position back. And we did that.
“Sticking to your values is most difficult in such circumstances, but we did that.
“Having done that and possibly wasting three points in what looked like would have a tough championship made him come back very strong after the season break at Spa.
“And from then on it was rock and roll.”
Mercedes are tipped to dominate once again in 2018, with Hamilton and Bottas already working with the mechanics on their new cars.
But the Silver Arrows endured a tough start to the 2017 campaign as problems in the car, which Wolff once described as “gremlins”, persisted.
And the team chief was all praise for his two drivers for how they turned the season around.
“With a car that was difficult at the start of the season Lewis extracted what he could have from the car,” Wolff said of Hamilton.
“But it was difficult for both drivers to understand how to drive a car that was capricious.
“Fast but difficult at times. So we saw variability in performances.
“In Monaco our car was almost undrivable. But Lewis started to understand the car after a handful of races and how he needed to drive the car to keep the tyres in the right window, and then become better and better.”