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.
Nicolai Muller fired wide for the hosts three minutes later, but chances were otherwise at a premium early on.
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.
Dortmund responded instantly, with a well-worked counter-attack allowing Henrikh Mkhitaryan to get behind the defence and pull back for Shinji Kagawa in the six-yard box, but he failed to produce a decisive touch.
Aubameyang warmed the palms of Jaroslav Drobny prior to the interval with a drilled effort, but Hamburg's Czech goalkeeper remained largely untested.
Dortmund introduced Kevin Kampl at the start of the second half and the Slovenian nearly made an impact on 55 minutes, firing just wide from the edge of the area, before Reus spurned another opening two minutes later.
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.
