Captain Root insisted his team can continue their upward curve after beating India by 60 runs at the Ageas Bowl and seizing an unbeatable 3-1 series lead.
Moeen took 4-71 – and 9-134 in the match – and his haul in his first Test of the summer included the match-changing wicket of Indian skipper Virat Kohli for 58.
It means England have beaten the world’s No.1 ranked Test team with Friday’s final match at the Oval still to be played.
Root said: “I think it has been my best and most enjoyable win. I feel like I’ve had quite a big input and felt in control of things. I have a real clear vision of how I see us improving as a group long-term, it’s a really exciting time for me and the team. We have guys who are willing to buy into that.
“We have a realistic understanding of where we are currently and where we can get to. This victory is a big step in the right direction and we can go from strength to strength. We are always searching for improvement and there have been areas in this series where we’ve not been as good as we’d like. But we are heading in the right direction.
“And this series must have been very exciting for people sitting at home. It shows Test cricket is still alive and kicking, to me it is very much the pinnacle of the sport.”
India, set 245 for victory, lost three quick wickets but a fourth-wicket stand of 101 between Kohli and Ajinkya Rahane gave them hope.
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Root added: “I was confident that, if we bowled to our potential, we’d have enough runs to get across the line. The biggest challenge was staying calm and trusting that the wicket would help us.
“Moeen was superb. Sometimes, having a bit of time away from the Test cricket can be a really good thing. He was in the form of his life for Worcestershire and he’s taken that into this match. I couldn’t be more pleased for him. He’s such a big part of this team.”
Kohli played with Moeen for Bangalore Royal Challengers in this year’s Indian Premier League – and they became big mates.
He revealed: “Moeen bowled really well, he was relentless with the areas and speeds he bowled.
“I really like the guy. I’ve never sat down and analysed his career. We never talk about cricket generally, we normally talk about other things.
He’s a lovely guy, very talented, that’s why he was picked in the IPL.
“This has been a competitive and hard-fought series and Joe told me that he agrees with that. The scorecard doesn’t always reflect the way the series has gone. The process has been very competitive, and it has been enjoyable.”
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