Evers gratefully accepted a cross from Sunderland striker Michael Bridges to fire the League's Under-21 XI ahead - ironically, Bridges will be face- to- face with the scorer in next week's Worthington Cup quarter-final at the Stadium of Light.
But 10 minutes from time the Serie B Under-12 side levelled the game with a penalty by Pescara teenager, Mauro Esposito. The game finished with honours even, but the Italian substitute Antonio Bellavista was sent off for a second bookable offence just 20 minutes after coming on to the field.
Evers' goal was his fourth of the season and a deserved reward for an industrious display in central midfield for the England Under-21 coach, Peter Taylor, who was in charge of the side.
The Hitchin-born player almost missed out as Michael Branch prepared to latch on to Bridges' ball. But a loud shout by Evers led to the Everton striker stepping over the ball for Evers to strike crisply past Napoli goalkeeper, Ferdinando Coppola.
Previously it was the man at the other end of the field, the Nationwide captain, Richard Wright of Ipswich, who had kept his side in the game with fine saves from Vincenzo Italiano and Claudio Ferrarese.
But Wright, who was a substitute for the full England side last week, could do nothing to stop Esposito's penalty in the 80th minute after the Norwich defender Lee Marshall had been harshly adjudged to have fouled Ferrarese in the area.
The Italian side were let down when second-half substitute Bellavista clattered into Bradford striker Isiah Rankin to earn his second yellow card in 20 minutes.
The hosts had controlled the game in the first half, but the Nationwide League's defensive marshalling by Simon Marsh, of Oxford, Bradford's Andy O'Brien and Marshall meant Wright was quiet in goal.
In the second half the League Select XI began to enjoy more possession and Evers' goal was the perfect reward for their composure.
On the hour Branch proved just why Manchester City have had two bids to make his loan move permanent rejected by Everton when he forced a fine save from Coppola.Reuse content