Hamilton lamented over the radio that he was not sure the tyres would make it to the end of the grand prix - however the Briton fended off Vettel and Bottas to take his tenth win of the 2019 season.
While Wolff admits he had doubts over the strategy, he insisted it was easier to take risks when they are not leading the race.
"No we were not convinced," he said. "There were two main factors. We knew that we had to take a risk when you are starting third and sixth it is easier to come up with some bold strategies provided that you have a good car which we had today and fantastic drivers.
"We knew we had to do something different. Then we saw Ricciardo going long on the hard tyres with intriguing lap times. Then we had quite some discussion and at the end what James and his strategy partner opted for was to go long worked out."
Wolff hailed Hamilton's efforts in getting the hard tyre to the end on such a long stint, but believes it "makes sense" when looking at the data from Ricciardo and Max Verstappen.
"I have complete faith in him but we knew it was going to be stretched and even the best driver needs to rely on the material and 47 laps sounded like [a lot].
"When you look at the data of the first stint and Ricciardo and Max going strong it kind of makes sense. Still, 47 laps sounded like an awful lot of laps."
Bahrain International Circuit - Winter testing