With Viking top of the table and both sides competing in the league phase of this year's Champions League, the rivalry between them has reached fever pitch.
Falchener turned the ball into his own net in the fourth minute to give Bodo/Glimt an early lead and Andreas Helmersen added a second 15 minutes later, but champions Viking levelled through Kristoffer Haugen and Erik Botheim.
The home fans at the Aspmyra Stadium erupted in celebration when a shot from Jens Petter Hauge deflected off Falchener and past his goalkeeper in the 43rd minute for what looked like another own goal, but Hauge was credited with the strike.
Tempers boiled over on the sideline in first-half stoppage time after a brutal tackle on Hauge by Viking's Kristoffer Askildsen, and Bodo/Glimt coach Kjetil Knutsen and his Viking counterpart Morten Jensen were shown red cards after an angry confrontation that saw Knutsen pull down the peak of Jensen's cap.
"It was a bit comical. We talked about it before the game, that we and the coaching team had to keep our heads cool," Bodo/Glimt captain Patrick Berg told broadcaster TV2.
"At least we managed it out on the field - I haven't seen the situation, but it's clear that Kjetil didn't manage it as well as we did."
The second half contained plenty more fiery football and crunching tackles, but no more goals, and the home win for Bodo brings them level on points and goal difference with Viking at the top of the table.
Viking remain in first place thanks to a 3-0 win over Bodo in Stavanger earlier in the season.