The result left Paderborn bottom of the table on 20 points with two games to play, eight points adrift of the relegation playoff spot occupied by Fortuna Duesseldorf.
Union Berlin are safe after climbing up to 12th on 38 points.
The hosts’ domination was rewarded in the 27th minute when Ben Zolinski headed a Christopher Trimmel free kick into his own goal.
Union Berlin went close to doubling the tally on 73 minutes, only for Robert Andrich’s attempt to hit the post, leaving Paderborn with an outside chance to turn it around.
Yet Paderborn, who needed to win to keep their hopes of staying in the top flight alive, never threatened a comeback.