Neville's praise comes after Mourinho masterminded a 1-0 victory at Manchester City on Monday evening, ending the Sky Blues' 20-game unbeaten run in the process.
Speaking on Monday Night Football, Sky Sports analyst Neville said: "He was like the conductor of the orchestra. He walks out at the start of the match and sits on the bench before his team have even come out.
"He comes alive on big match days and that's what the best managers do. He is the best in the world at the moment at affecting big matches, absolutely brilliant.
"He thinks about every small detail, things that I don't think many would think of because he's been around the block. He's shrewd, he's smart and he calls it on. He's good and he knows he's good."
Chelsea, who have now won eight of their last nine games in all competitions, currently sit third in the Premier League table, level on points with City and two behind leaders Arsenal.