The former Bolton forward, who was included in the Mainz starting XI for the first time this season, brought Thomas Tuchel's side level before half-time after a Bo Svensson own goal had put the hosts in front early on.
Fortuna arguably enjoyed the better chances of the game, but they were unable to find a way through as they picked up a rare draw to edge seven points clear of the relegation zone.
The draw moves Mainz to within two points of the top six and goes some way towards making up for their midweek defeat to Freiburg in the DFB-Pokal.
Mainz could hardly have imagined a worse start to the game as goalkeeper Christian Wetklo found himself fishing the ball out of the net in the sixth minute when Svensson's flick took the ball into his own goal.
Mainz suffered from that early blow but managed to weather the storm and keep a buoyant Fortuna side at bay.
Shortly before the interval, the visitors got the break they needed when a low cross from Marco Caligiuri, who had only been on the field a few minutes, was missed by Fortuna goalkeeper Fabian Giefer and Klasnic was on hand to open his account for the season.
His last goal in the Bundesliga had come during his Werder Bremen days at the end of the 2007-08 season, and this was his 50th strike in Germany's top flight.
It did not seriously alter the tone of the game, though, as Fortuna continued to dominate proceedings.
Their only fault was not producing the finish all of their hard work merited and, after a frustrating second 45 minutes, they had to raise the white flag and accept only a point at the Dusseldorf Arena.