A further double from Henrikh Mkhitaryan and a goal for Manuel Friedrich earned BVB a morale-boosting victory against a hapless home side, who scored late through Levent Aycicek
Robin Dutt's men threatened early on, but third-placed Dortmund rarely looked in danger of dropping points and Lewandowski's first league goal since November 30, after excellent work by Marcel Schmelzer, sent the visitors on their way in the 26th minute.
Mkhitaryan doubled Dortmund's lead just before the break, demonstrating quick feet on the edge of the area prior to a clinical finish.
Centre-back Manuel Friedrich then latched on to a corner early in the second half and tapped in at the back post for his first Bundesliga strike since January 2012, while Mkhitaryan grabbed his second after a sumptuous assist from Marco Reus.
Lewandowski got a second with five minutes remaining, and Levent Aycicek netted a consolation in the 89th minute for Bremen, who are in danger of being drawn into a relegation battle.
The hosts gave a debut to Ludovic Obraniak following his January arrival from Bordeaux, while Dortmund were without the services of Mats Hummels due to a foot injury.
After a cagey opening, Schmelzer robbed Theodor Gebre Selassie of possession near the corner flag before cutting a pass back to Lewandowski, and the Poland star confidently caressed a finish into the bottom-right corner.
Mkhitaryan should have finished a well-worked move in the 37th minute as he diverted Pierre-Emerick Aubameyang's header into the side netting, but made amends four minutes later.
The Armenian jolted past Assani Lukimya on the edge of the area and, having been afforded space by the home side's defenders, drove a low shot past Raphael Wolf and into the bottom-left corner.
Jurgen Klopp's side effectively wrapped up the three points three minutes into the second period as Hunt inadvertently flicked on a Dortmund corner and the unmarked Friedrich prodded home.
Things were in danger of getting embarrassing for Bremen and the visitors added a fourth just after the hour mark.
Reus produced a devilish back-heel into the area after receiving a pass from Mkhitaryan, and the former Shakhtar Donetsk man continued his run to collect the loose ball before delicately clipping past Wolf.
Lewandowski rounded Wolf and slotted through Sebastian Prodl's legs with composure to grab his second, but it was Bremen who completed the scoring as substitute Aycicek converted at the back post.