Assani Lukimya gave the visitors a ninth-minute lead when the defender beat Hamburg's Jeffrey Bruma to score with the back of his head.
Hamburg levelled with a stunning goal from South Korean Son Heung-min, who charged down the right and beat keeper Sebastian Mielitz with a surprise shot from a very tight angle.
The hosts got off to a flying start straight after the break with Dennis Aogo taking full advantage of confusion in the box to drill in from close range in the 46th minute and then set up Artjoms Rudnevs six minutes later.
Hamburg's celebrations were cut short with Werder defender Sokratis Papastathopoulos pulling a goal back in the 54th with a shot that slid under keeper Rene Adler's body.
Bremen, however, soon ran out of steam and were reduced to 10 men when captain Clemens Fritz was sent off with a second booking for a hard challenge in the 80th minute.
He was followed 10 minutes later by substitute Marko Arnautovic who was booked for a foul and then pretended to kick the ball at the referee who sent him off with a second yellow card.
Hamburg move up to 28 points in ninth place with Werder, without a win in their last four league games, in 12th on 22.
Leaders Bayern Munich, top on 45 points, can increase the eight-point gap over second-placed Bayer Leverkusen, who drew 0-0 at Freiburg on Saturday, when they travel to VfB Stuttgart later on Sunday.
Champions Borussia Dortmund are third on 36 after beating Nuremberg 3-0 on Friday.