Bielefeld keeper Dennis Eilhoff completely misjudged Piotr Trochowski's free kick and palmed the ball into his own goal for the 32nd minute opener while Peruvian Paolo Guerrero bagged the second with a well-struck left-foot effort in the 60th.
Bielefeld squandered a chance to level in the 55th when Artur Wichniarek had a penalty saved.
"We were dominant throughout the game but were lucky with our first goal and the saved penalty," said Hamburg coach Martin Jol. "I am happy to be in touch within striking distance of the top of the table and not having squandered any more points."
With the league's best home record this season -- eight wins and one draw before Sunday -- Hamburg looked for a quick goal from the start but Bielefeld had the best early chance when Jonas Kamper fired just over the crossbar in the 25th minute.
Bielefeld wasted a golden chance to make up for Eilhoff's blunder after the break when Hamburg keeper Frank Rost saved Wichniarek's weak penalty.
"If you want to have any chance against such top teams everything must work and today it didn't work for us," Bielefeld coach Michael Frontzeck told reporters. "We made far too many mistakes and did not use our chances to equalise."
