A tightly contested game saw the visitors dominate possession, with Pierre-Emerick Aubameyang and Marco Reus predictably at the heart of Dortmund's attacking efforts.
However, despite an early injury to Johan Djourou, a well-drilled Hamburg defence held firm, while Mohamed Gouaida and Zoltan Stieber were both denied by visiting goalkeeper Roman Weidenfeller.
The result deals a blow to mid-table Dortmund's hopes of securing European football for next season.
Relegation-threatened Hamburg, meanwhile, remain without a win in their last four games having drawn a 13th blank of the season.
Dortmund had won on only one of their previous nine visits to the Imtech Arena, and they once again found Hamburg in spirited mood.
Reus, passed fit after an injury scare in midweek, nearly contributed to an opener after three minutes, whipping in a wicked free-kick for Aubameyang, only for Djourou to make a crucial intervention.
Hamburg were dealt a blow on 18 minutes when captain Djourou was forced off with a head injury, but their disappointment could have been swiftly cut short had Gouaida not lashed an effort over.
Gouaida did manage to test Weidenfeller with his next effort, forcing a smart parried save with a stinging drive.
Aubameyang warmed the palms of Jaroslav Drobny prior to the interval with a drilled effort, but Hamburg's Czech goalkeeper remained largely untested.
Aubameyang planted a header just wide after 63 minutes and the visitors' profligacy in front of goal was almost punished when Stieber's curled 30-yard free-kick brought a fine save from Weidenfeller.
Klopp threw on Ciro Immobile and Jakub Blaszczykowski in a bid to find a winner, but Hamburg's defence could not be breached despite mounting Dortmund pressure.
