The hosts were without a league win since early November, but Justin Njinmah should have put them ahead after only 50 seconds when he side-footed just wide from 15 yards out following Jens Stage’s incisive pass.
Andrej Kramaric tested Mio Backhaus with a near-post header from a corner shortly after, yet chances were scarce in a low-quality first half until Alexander Prass lit up the Weserstadion with a moment of magic just before half-time.
Hoffenheim worked the ball to the edge of the penalty area, and Kramaric provided the perfect lay-off for the midfielder, who fired an unstoppable first-time shot into the top corner from 25 yards to score his first goal for the club in his 50th appearance.
A first-half goal was perhaps inevitable, with only two of Hoffenheim’s Bundesliga games this season reaching half-time goalless, and it put the onus on Werder for the second half.
The hosts were given a huge boost just six minutes after the break when Burger’s sliding challenge on Cameron Puertas was upgraded from a yellow card to a red following a VAR review, but they barely had the chance to make the most of their advantage before Hoffenheim doubled their lead.
Werder failed to clear a free-kick, and Grischa Promel gave Julian Malatini a nudge to send him off-balance, before lifting his sixth Bundesliga goal of the season past Backhaus.
Romano Schmid thought he had halved the deficit with a flicked finish just after the hour mark, but another VAR review showed the Austrian midfielder was marginally offside.
Werder never looked like getting back into the game despite making several attacking substitutions, and they remain 15th in the table as a result, just three points above 16th-place FSV Mainz.
The Weserstadion has become a happy hunting ground for Hoffenheim, who are unbeaten in 11 away H2Hs (W6) and now boast the second-best away record in the Bundesliga (W6, D3, L1), behind only Bayern Munich. This win keeps the visitors third in the table, trailing second-place Borussia Dortmund by just three points.
Flashscore Man of the Match: Alexander Prass (Hoffenheim)