Everitt's strike came minutes after Duncan Hodge had edged Scotland ahead, 22-19, with a penalty that went over with the aid of an upright.
Ireland trailed 12 -5 at half-time and ended the half with 14 men when Jeremy Staunton was yellow-carded for a deliberate knock-on. However, within minutes of the re-start they had drawn level thanks to a James Topping try, converted by Everitt, and shortly after went into the lead when Rob Henderson scored his second try of the game.
Jason White scored two first half tries for the home side before himself earning a yellow card in the second half.
Earlier in the afternoon, coach Michael Bradley's tenure in charge of the Ireland Under 21s got off to an ideal start with a 13-5 win over Scotland in Dundee.. The Irish led 6-0 at the break thanks to two penalties from out-half, David McAllister and although the Scots struck late to score a try, the Irish responded superbly, to score a try of their own deep in injury-time, through Richard Lane to seal a deserved victory. McAllister added the points