With DIF trailing 2-1 in the middle frame, Davidsson took a long stretch pass at the FBK blue line and quickly connected with his brother streaking to the right post to tie the game.
In addition to the assist, Davidsson also won seven of his eight face-offs while skating for a season-high 12:52.
Farjestad centerman Rasmus Asplund fired one shot on goal for the winning side. Through eight games, Asplund has collected three goals, eight points and a plus-9 rating.
Elsewhere in Sweden, Victor Olofsson produced three shots on goal as Frolunda fell to HV 71 3-1.
In the WHL, Brandon Hagel racked up three helpers as Red Deer got past Kootenay 5-4. Hagel now has 11 points (3+8) in eight games to become the first Sabres prospect this season to hit the double-digit point barrier.
Cliff Pu extended his season-starting goalless streak to seven games as London was defeated by Windsor 3-1. Pu has recorded just three assists in those seven games.
Austin Osmanski logged one shot on goal and a minus-1 rating as Peterborough edged Kingston 2-1.
On Wednesday, Ukko-Pekka Luukkonen started his fourth consecutive game. stopping 42 of 47 shots as LeKi dropped a 5-1 decision to Kiekko-Vantaa. The loss, Luukkonen's first of the season, drops him to 4-1 with a 2.36 GAA and .931 save%.
