The Sweden international, who had conceded 14 times in his first four appearances for the club, retained his place in the team despite the availability of No.1 Emi Martinez following his return from the World Cup.
And he played his part in a confident Villa display as they limited Tottenham to few chances before going on to win the match through second half goals from Emi Buendia and Douglas Luiz.
Martinez, who returned to Bodymoor Heath last Friday, may yet reclaim his starting spot for Wednesday’s derby with Wolves.
Emery said: “Our plan was always to give Emi a rest after the World Cup. With Robin we were working as well and trying to give him confidence. He will get confidence from playing in matches.
“He really deserved his clean sheet and his performance was excellent as well.
“Emi is going to train with us tomorrow and on Tuesday and will be closer to playing with us. But after today, we can have belief in Robin Olsen. Emi is very important. He is the No.1. Robin knows his role and is very positive as a person. His role is very important as well. In matches like today when we needed his performance, he was fantastic.”
Villa were deserving of their third win in four matches – and second straight away from home in the Premier League - since Emery took charge at the start of November.
A delighted boss said: “Away from home is our big challenge. This match, we were speaking about it and about where is our level? How can we show our level playing against top six, Tottenham, and being away as well?
“It is about being competitive and deserving to win. You can win but you don’t deserve it sometimes.
“Today, we deserved it because we played a really competitive game defensively and we had chances as well to score and we were clinical.
“We were speaking about the match we played against Liverpool on Monday and we weren’t clinical. Today, the players had this challenge.
“We spent New Year’s Eve in London in the hotel. We wanted to show our quality and I think the players gave a really good performance.
“They fought and they were so, so confident in our defensive moments. When we could add attacking moments. It was a really good performance.”