The German-born Turk, 19, opened the scoring with a 35-metre strike after 20 minutes that took Diego Benaglio by surprise, with the Switzerland keeper running back to his goal only for the ball to bounce off the bar on to his head and into the net.
Wolfsburg, now unbeaten in their last six league games, levelled in the 31st with a Ricardo Rodriguez penalty after a foul by Heiko Westermann.
Hamburg stormed forward late in the game as Wolfsburg ran out of steam and could have snatched the win after Calhanoglou and Pierre Michel Lasogga outfoxed the home defence only for Ivo Ilicevic to hit the bar when faced with an open goal.
The result leaves Wolfsburg fifth on 23 points, two points behind Borussia Moenchengladbach in the Champions league spots, with Hamburg climbing one place to 10th on 16.
Bayern Munich, four points clear at the top on 35 points host bottom side Eintracht Braunschweig on Saturday (1430GMT).
Second-placed Bayer Leverkusen will expect a reaction after a 5-0 midweek Champions League home defeat by Manchester United when they host second-bottom Nuremberg while Borussia Dortmund, in third a further three points off the pace, visit Mainz 05.
- Sports & Recreation