Heiko Westermann nodded Hamburg into a half-time lead but the visitors extended their unbeaten run to eight games thanks to Makoto Hasebe's leveller.
The result means Hamburg are three points behind sixth-placed Freiburg, who, as it stands, occupy the final Europa League spot. Freiburg also have a vastly superior goal difference with just two games to go.
Hamburg's inability to secure the win they craved may be partly explained by a list of absentees which deprived coach Thorsten Fink of suspended goalkeeper Rene Adler and injured quartet Michael Mancienne, Marcell Jansen, Dennis Aogo and Tolgay Arslan.
Fielding a weakened side did not adversely affect the home side early on as they made an aggressive start which would have been capped with a goal had Rafael van der Vaart's fourth-minute volley not been superbly kept out by Wolfsburg goalkeeper Diego Benaglio.
They threatened again in the 20th minute when fine interplay between Son Heung-min and Artjoms Rudnevs enabled the South Korean to bear down on goal. He attempted to round Benaglio but, having fallen to the turf, earned only a yellow card for a perceived dive.
Vieirinha and Diego had long-range efforts as Wolfsburg finally earned a foothold in the game but, at the other end, only a fine block from Naldo prevented Rudnevs from opening the scoring.
Hamburg goalkeeper Jaroslav Drobny had to be alert to deny former Hamburg striker Ivica Olic after a slip from Westermann before the Germany international made amends on the stoke of half-time by heading home Van der Vaart's free-kick.
Dennis Diekmeier ought to have doubled their advantage within a minute of the restart but shot over the bar from 10 yards.
Wolfsburg boss Dieter Hecking brought on Ivan Perisic for Olic and the move paid instant dividends when he crossed for Hasebe to send a diving header past Drobny.
The visitors poured forward in search of a winner but found Drobny in fine form.
First he saved Naldo's effort and then came out on top in a one-on-one with Bas Dost.