John Rooney's early penalty for the hosts was cancelled out by Richard Brodie before the break.
Newton rose to meet Rooney's corner to reclaim the lead midway through the second half.
It was the first time Wrexham manager Gary Mills had faced former club York, who sacked him three-and-a-half years ago.
Mills guided York to promotion into League Two and won the FA Trophy in 2012, but was dismissed 10 months later.
Alex Whittle (York City) is shown the yellow card for a bad foul.
Substitution, Wrexham. Callum Powell replaces Tyler Harvey.
Second Half begins Wrexham 1, York City 1.
First Half ends, Wrexham 1, York City 1.
Substitution, York City. Clovis Kamdjo replaces Yan Klukowski.
Richard Brodie (York City) is shown the yellow card for a bad foul.
Goal!  Wrexham 1, York City 1. Richard Brodie (York City).
Goal!  Wrexham 1, York City 0. John Rooney (Wrexham) converts the penalty with a.
First Half begins.
Lineups are announced and players are warming up.
Captain Sean Newton headed Wrexham to victory over visitors York City in the National League.