The England captain bowled 44 overs at Lord's, the most of any bowler in the match, and took five wickets to guide the hosts to a 22-run victory and 2-1 lead in the five-match series. He contributed 44 and 33 runs and was named player of the match.
The 34-year-old underwent a successful operation on a torn hamstring in December before undergoing a physical fitness programme during which he lost 10 kg.
"He's just desperate to be the man and make things happen," former skipper Root told BBC Sport.
"Incredible effort to be able to do that. I was just panicking that he wasn't going to make it through the game after a couple of bad injuries but he clearly trusts his body now.
"It's a great sign for us moving forward. I mean it really is isn't it, because that's back to his best."
The fourth Test begins on July 23 at Old Trafford.
