Danny Wilson's side have been at the foot of the table since 4 October following their 5-0 hammering at Arsenal, but with Bolton not playing until today and Crystal Palace having been beaten by Coventry, the Tykes can now see a gap between themselves and the top of the First Division.
They are now unbeaten at Oakwell since 29 November, while a remarkable FA Cup run has given them the confidence for the matter of a Premiership survival fight.
Wimbledon, who had won two and drawn two of their last four League games, know they cannot afford many more slip-ups if they are to avoid being drawn into trouble.
As he is Cup-tied, Fjortoft has flitted in and out of the side, but the Norwegian international made the most of this opportunity, scoring his first in the 25th minute, lofting his close-range shot over goalkeeper Neil Sullivan after being set up by Nicky Eaden and Clint Marcelle.
Barnsley, put under enormous pressure during the second half, managed to grab a bizarre match-winning second just after the hour. Darren Barnard's free-kick from the halfway line was floated into the penalty area, with Sullivan dropping the ball while under challenge from Marcelle.
As the Wimbledon players looked to the referee for a foul, the loose ball seemed to drop on to the leg of Fjortoft before trickling over the line.
Eight minutes later Wimbledon halved the deficit when Jason Euell headed in Kenny Cunningham's cross at the far post for his eighth of the season. It was backs to the wall defending in the closing 20 minutes, but Barnsley held on.Reuse content