Wolves, who made nine changes from Sunday’s Championship win over Sheffield United, made the brighter start but suffered a blow when key striker Raul Jimenez went off injured in the 37th minute.
The Mexico international’s replacement, Adam Armstrong, had a one-on-one effort saved low by Everton keeper Jordan Pickford in the 54th minute.
The hosts, who made six changes from the goalless draw with Tottenham in the Premier League, were frustrated as Virginia shone on his return to Merseyside.
James Garner had an effort on goal and Michael Keane headed just wide, before Virginia foiled substitute Brennan Johnson when the forward broke through.
Jack Grealish, who started his first Everton game since January following his loan return from Manchester City, played for 76 minutes before he was replaced by Tyrique George.
Everton face Ipswich Town on Saturday (15:00 BST) in the Premier League, while Wolves host West Brom in a West Midlands derby (12:00 BST) on Sunday in the Championship.