The Bundesliga title holders did just enough to claim victory in the German capital, as the winger's overhead volley made the difference on the day
With Shinji Kagawa and Mario Gotze sidelined, and Lukasz Piszczek forced off at half-time, Jurgen Klopp's side overcame the odds as they handed a sixth consecutive defeat to the hosts.
Nearly three quarters of the match passed with limited chances on goal, but Kevin Grosskreutz put the visitors ahead on 66 minutes and BVB held on to claim three points and maintain their spot atop the Bundesliga table.
Neither side looked like scoring in the first half and chances were few and far between. Lukasz Piszczek did well to cross from the end-line on eight minutes, but Lucas Barrios wasted the full-back's cross with a header that Thomas Kraft easily claimed.
On the half hour mark, the BVB pair combined again, but Barrios tripped over the ball and it was again easy work for the Hertha goalkeeper to claim.
Hertha nearly opened the scoring on 36 minutes as Mats Hummels was dispossessed in his own penalty area by Raffael, but Roman Weidenfeller made a strong challenge to deny the Brazilian. Moments later, there was a goalmouth scrap at the opposite end, but Barrios had a shot blocked and danger was averted.
Piszczek was again close to creating an opportunity on the stroke of half-time, as Robert Lewandowski played him in on goal, but Kraft was quick off his line to block the full-back's attempt. Piszczek was injured in the process and would not return in the second half.
After the break, Dortmund's lapses in concentration continued at the defensive end, as Neven Subotic and Hummels both had slip-ups that led to chances for Patrick Ebert. The right-winger received a well-weighted pass from Adrian Ramos on 50 minutes before flashing an attempt wide of the far post and three minutes later had a similar result.
Hertha would rue their missed chances as Dortmund would instead be first to score. Jakub Blaszczykowski crossed to Lewandowski, whose header was brilliantly saved by Kraft, but rebounded off the bar. Grosskreutz was first to the ball and struck an overhead volley past the Hertha No. 1 and into the net.
Entering the final stages of the game, the hosts looked dangerous and would not give up hope. Raffael was through on goal with 15 minutes left to play, but stumbled and back-heeled a pass when no team-mate had followed his run.
The win sees Dortmund remain first in the Bundesliga, regardless of other results, but comes at a cost as Piszczek joins Shinji Kagawa and Mario Gotze on the club's injury list. Hertha remain 15th, just two points ahead of the relegation zone.