The Polish striker scored midway through the first half with a header for last year's play-off contenders and then laid on the second for Dane Morten Bisgaard six minutes before the interval.
Although Argyle, who had four points from their first two games, rallied late on, some fine goalkeeping from Lee Camp ensured that Brown, former assistant to Sam Allardyce at Bolton, added a win to two earlier draws.
Plymouth forced four corners in the opening 75 seconds but that was really as good as it got for the home side in the first half.
Rasiak headed Adam Bolder's cross straight at Argyle goalkeeper Romain Larrieu to give Argyle a warning of what was to come and Bolder was then denied a penalty, when he was clearly fouled by Mathias Doumbe, before the visitors took the lead.
Richard Jackson crossed to the far post, where Rasiak looped a header over Larrieu, despite the Frenchman getting his fingertips to the ball and diverting it on to a post.
Rasiak then headed a similar cross from Tommy Smith back across the goal where Bisgaard chested the ball into the net.
Former Rangers midfielder Bojan Djordjic should have pulled one back in the second half when he wasted a free header from Akos Buzsaky's deep cross as Argyle came right back into the game.
Micky Evans was twice denied by Camp, who first blocked a fierce shot and then dropped on a long-range free-kick from Argyle skipper Paul Wotton.