The England international made his debut in Manchester United’s 4-0 victory over Chelsea FC at Old Trafford on Sunday afternoon.
Maguire started alongside Sweden international Victor Lindelof at centre-half for the club’s opening fixture of the Premier League season.
The 26-year-old didn’t put a foot wrong against Chelsea FC striker Tammy Abraham as Manchester United managed to keep a clean sheet.
Goals from Marcus Rashford, Anthony Martial, Daniel James secured a resounding victory for the hosts in their Premier League curtain raiser.
Maguire moved to Manchester United in a £80m deal from Leicester City earlier this month to become the world’s most expensive defender.
And former Manchester United defender Neville was impressed with Maguire’s debut after the Red Devils eased to a huge win over their top-four rivals.
“Maguire looks secure and he looks strong,” Neville told Sky Sports.
“Every time the ball came near him in the air he won it and he never looked any different to how he was for England or Leicester.
“I think that was the main thing; coming here with a huge price tag in a big game as a Manchester United player for the first time it didn’t look like anything had changed.
“He has a really good temperament. The hope is that he doesn’t just do his job, but he is a catalyst for strengthening the whole team. The great centre-backs I played with didn’t just help themselves during the game, they also had a big impact on others. We have spoken about Virgil van Dijk doing that at Liverpool.
“It’s too early to say Maguire will make the same difference as Van Dijk, but there’s a chance.
“Manchester City wanted Maguire and Manchester United won him and they so needed him. A character, a personality, a leader, a dominant force, he will bring stability to the club for the next five or six years.”
Manchester United signed Swansea City winger James, Crystal Palace defender Aaron Wan-Bissaka and Leicester centre-half Maguire in the summer.
Encouragingly for Manchester United, all three summer signing acquitted themselves well against Frank Lampard’s side.
Manchester United will take on Wolves in their next Premier League fixture at Molineux Stadium on Monday 19 August.
Ole Gunnar Solskjaer’s side will be looking to secure a return to the top four after their sixth-placed finish last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news