Hamburg boost survival chances
Hamburg's goalkeeper Rene Adler celebrates after their German first division Bundesliga football match against Bayer Leverkusen in the northern German city of Hamburg on April 4, 2014 - by Oliver Hardt
Defender Heiko Westermann grabbed the 82nd-minute winner with a magnificent volley from a cross by substitute Tomas Rincon.
Turkish midfielder Hakan Calhanoglu had opened the scoring after just four minutes for the 1983 European Cup winners.
The 20-year-old found the net with a sharp drive.
However, Leverkusen were level on 58 minutes when 18-year-old striker Julian Brandt beat Hamburg keeper Rene Adler.
Leverkusen piled on the pressure late in the game but Adler pulled off a series of impressive saves.
Hamburg, the only team never to have been relegated from the German top flight, have 27 points and moved fourth from bottom.
Leverkusen remain in fourth place -- the last Champions League spot -- but can be overtaken by Wolfsburg who face Borussia Dortmund on Saturday.
Hamburg are on their third coach this season after Mirko Slomka took charge last month following Bert van Marwijk's dismissal in February, while Thorsten Fink was sacked in September.