Dieter Hecking's side jump into fifth to apply extra pressure to free-falling Bayer Leverkusen, with goals coming either side of the break through Junior Malanda, Ivan Perisic and Maximilian Arnold.
Werder's only reply came from Sebastian Prodl.
The Wolves wasted no time in forging a lead from their first opportunity in the opening 100 seconds as Malanda headed past Raphael Wolf with the aid of a deflection.
Bremen lacked inspiration early doors and were two behind before 10 minutes had been played following a super, crisp attack from Wolfsburg. Right-back Christian Trasch forced the issue, linking with Arnold, who laid off delicately for Croatian Perisic to slam into the net.
Credit has to be afforded to Robin Dutt's side for their reaction to the second goal because the margin was slashed within six minutes when Sebastian Prodl took advantage of indecisive goalkeeping from Diego Benaglio to score.
Benaglio, Wolfsburg's Swiss skipper, was on the verge of coming off with five minutes left in the first half due to a niggling injury problem.
After the restart, Wolfsburg started on the front-foot with Werder's Clemens Fritz blocking well to prevent Daniel Caligiuri from hitting the target.
Caligiuri is normally a reliable finisher from inside the penalty area, but he missed an almost open goal after the hour mark as he struggled to control his balance.
Wolfsburg then capped a fine evening's work through Arnold's well-struck left-foot shot which found the back of the net.