Hamburg, the only ever-present club since the Bundesliga was created in 1963, are now in 15th place, a point above the relegation playoff spot, after spending weeks languishing in the bottom three.
Leverkusen are fourth on 48 points and coach Sami Hyypia's future could be in doubt following a woeful sequence of one win in nine league matches.
Hamburg, missing half a dozen players through injury including striker Pierre-Michel Lasogga, got off to a dream start when Hakan Calhanoglu slotted his ninth league goal of the campaign in the fourth minute.
The home side then sat back, allowing Leverkusen far too much space to attack.
Hyypia's team had a golden chance on 35 minutes but keeper Rene Adler fisted away a close-range header from Son Heung-min.
Leverkusen finally levelled when Julian Brandt, making his first start, took a pot shot from 25 metres and Adler let the ball slip through his hands in the 58th minute.
Hamburg then went back in front when Westermann drilled in a perfect right-foot volley from eight metres after a fine cross by Dennis Diekmeier.
Champions Bayern Munich travel to Augsburg on Saturday when second-placed Borussia Dortmund entertain VfL Wolfsburg.
- Sports & Recreation
- Sami Hyypia
- Hakan Calhanoglu