The Argentinian forward marked his first start for the Bavarians with the only goal of the game to take Markus Weinzierl's men onto 20 points for the season, halfway towards their overall goal for the whole campaign with two games still to play before the midway stage.
Bobadilla was a threat throughout as Hamburg struggled to match their own fans' expectations once again.
The Argentinian, who picked up an injury in his first game after joining from Basle in the summer, looked motivated from the get-go.
He sent in the first dangerous shot which Rene Adler managed to tip over the crossbar at full stretch in the 14th minute.
Just four minutes later, Bobadilla opened his account for the club, turning the ball in at the far post from Halil Altintop's low cross after Tobias Werner expertly let it go.
Altintop nearly headed Augsburg two in front as they showed no fear at the HSV-Arena, taking the game to their hosts with authority and menace.
Werner nearly doubled their lead early in the second half, but Adler denied him before another Werner effort hit the crossbar.
Hamburg struggled to respond and the Augsburg defence was rarely breached.
With a total of only eight shots compared to Augsburg's 16, the hosts could have no complaints about being beaten once again as they fell to within five points of the bottom three ahead of Freiburg's meeting with Wolfsburg on Sunday.