The Seagulls midfielder gave his side the ideal start after just 90 seconds, as he cashed in on slack defending to head in a corner by Kevin McLeod from six yards.
Barnet had a lucky escape in the eighth minute when Nicky Forster headed another McLeod corner against the bar.
A superb run by Barnet's Albert Adomah created an opening for Joe Tabiri to level after 18 minutes, but he failed to convert from inside the six-yard box.
Forster latched on to a clever flick from strike partner Glenn Murray to double Brighton's lead in the 28th minute with a fierce shot to the right of keeper Rob Beckwith.
Virgo added his second seven minutes later with a powerful far-post header following another corner by McLeod, before Matt Richards added a fourth two minutes before the break with a free-kick from just outside the area.