Danish Marcus Ingvartsen gave the Berlin team the lead and in the 45th minute Andersson nodded 2-0 neatly on the corner.
Shortly thereafter, he repeated the business as he nodded 3-0 on away.
Mainz then reduced through Karim Onisiwo.
Andersson has now scored five goals in this year's Bundesliga and thus passes Quaison as the best Swedish goal scorer in the German high league.
Mainz has been tough on negative qualifying and Union Berlin is four points ahead of them.
The match is ongoing