Gate suffered a disappointing defeat on their return to School Road after three away games.
Promoted Barnton, who started the day second-bottom of the Hallmark Security League premier division without a win in six games, scored late in each half on their first visit to Blackpool.
Gate made a bright start but struggled to make their pressure count, Andrew Richards firing wide after five minutes.
The Cheshire club had their first chance five minutes later but Ben Fletcher saved the shot comfortably.
Visiting keeper Matt Conkie was also up to his task when Brett Dawson played Ben Seear through.
Conkie was outstanding in the first half , alert to all Gate’s threats, and his side took the lead in the dying seconds of the half.
A ball through the middle found striker Chris Smith, who took a touch and lifted the ball over the onrushing Fletcher.
Gate lost their momentum after the break and couldn’t rreally find a spark until the 74th minute, when 15-goal top scorer Ric Seear headed over from Seydou Bamba’s cross.
Gate’s best chance of an equaliser fell to Dawson, who collected Ryan Riley’s lovely crossfield pass, beat his man on the edge of the box but fired into the side-netting from a tight angle.
Barnton sealed the points six minutes from time, when Jonathan Jones chipped over Fletcher as he came out to narrow the angle.
Midtable Gate will be looking to bounce back at Padiham on Wednesday (7.45pm).
Gate: Fletcher, Richards, Carroll, Alexander, Bamba, Hall, Thornber, B.Seear, Riley, Dawson, R.Seear; subs: Higham, Noblet, Tanser, Buchan.