Simon Davey's unlikely high-fliers looked set to slump to a rare defeat when Mostto, a £400,000 summer arrival from his homeland finally found the mark.
Burnley claimed an early lead that left Barnsley feeling hard done by after two controversial penalty decisions went the way of the visitors.
After ten minutes Barnsley striker Kayode Odejayi was given a mauling by Clarke Carlisle but ref Lee Probert dismissed claims for a spot-kick.
Barnsley were still protesting as Burnley hit them on the break less than 60 seconds later.
Wade Elliott's cross was whipped in from the right and was met by defender Lewin Nyatanga who tried to hook it clear. However, the ball ricocheted against Andy Gray and shot past the keeper for the big striker's eighth goal of the season.
The Tykes' second claim for a penalty came immediately after the goal when Carlisle clashed with Mostto who went down but the home side were again denied the decision.
The goal boosted Burnley and left the home side, who started the game in sixth position in the table, feeling sorry for themselves.
A 25-yard shot from Elliott went close to stretching the Clarets' lead before a well-worked move found him in another good position but he drilled wide after spinning well on the edge of the box.
And when Alan Mahon and Stephen Jordan linked smartly, Jordan fired over before Gray was within a whisker of a second but his header was well-saved by Heinz Muller.
A long-range effort from Chris McCann was easily held by Muller and a Mahon corner was headed over by Carlisle.
Barnsley had their first shot on target when a cross from Jamal Campbell-Ryce was cleared as far as Brian Howard whose shot was blocked and Gabor Kiraly held onto a fierce follow-up effort from Dominik Werling.
Grant McCann almost scored when his dipping effort from the edge of the area was saved by Kiraly, but after 71 minutes Barnsley found the mark when Mostto stole in to head home the rebound after Nyatanga's header from a Brian Howard corner had hit the bar.