The visitors immediately took control of the game and thought they had the lead inside seven minutes, but Christoph Baumgartner had strayed offside before slotting the ball home.
They weren’t to be denied for long however, as two minutes later Willi Orban’s attempted cross from the left surprised everybody to float all the way into the far top corner to put Leipzig ahead.
Their fast start got even better as they doubled the lead in the first fifteen minutes; this time, Antonio Nusa pounced on a loose ball and slammed it home from the edge of the area, giving Patrick Drewes no chance.
The shell-shocked hosts tried to work their way back into the encounter, but things went from bad to worse after just twenty minutes as Baumgartner finally got himself on the scoresheet for real, tapping home from close range.
Bochum’s luck was summed up just before half-time when Baumgartner deflected a corner towards his own goal with his arm, only for Peter Gulacsi to make an outstanding stop, while the VAR review decided there was no reason to award a penalty.
Dieter Hecking responded at the break by introducing Gerrit Holtmann to the home attack, and it proved to be an inspired sub as Bochum struck three times before the hour mark.
Holtmann played his part by teeing up Myron Boadu for a tap-in straight after the restart before the Dutch striker pounced again to poke home from a few yards out.
Leipzig were rattled, and their capitulation was complete moments later when Boadu confidently tucked a penalty into the back of the net after a clumsy challenge by Nusa.
Bochum remain bottom, but after failing to record a win in their opening 15 league games this season, they now sit only four points away from the relegation play-off spot. Leipzig, meanwhile, are still in fifth place having missed the opportunity to leapfrog VfB Stuttgart in the table and will struggle to comprehend how they squandered such a lead.
Flashscore Man of the Match: Myron Boadu (Bochum)