Rögle looked to be 2-0 ahead of the third period when Martin Johansson reduced for Färjestad with only two seconds left of the second period.
The home team gained momentum and eight minutes into the third period, the Värmlands had taken the lead with 4-2.
Series leader Rögle showed character and goals by Olli Palola and Daniel Zaar forced an extension, but there FBK decided after only 1.10.
Jacob Nilsson won the puck in his own zone and then ran all the way across the ice and outsmarted goalkeeper Christoffer Rifalk with a backhand.
With the victory, Färjestad climbs up to sixth place in the SHL.
Rögle is still in first place, one point ahead of Frölunda and with two games less played.
The text is updated.