A bogey at the last cost Bjorn the outright lead meaning he and Gallacher share a one stroke advantage at 11-under par over a group of five players.
Danny Willett, Victor Dubuisson, Richard Finch, Tommy Fleetwood and former winner Miguel Angel Jimenez – who also dropped a shot on the 18th – finished nine under after two rounds.
"I played better today than yesterday, although at the end it wasn't the prettiest,” said the Dane.
"I stayed patient and tried not to make any silly bogeys, but I made one down the last. I'm happy with the way I'm playing, I've been steady rather than spectacular."
Francesco Molinari and Darren Clarke missed the half-way cut.