United looked to have done enough for a draw after restoring parity through Jesús Gámez midway through the second half, but former Middlesbrough frontman Fischer had the final say.
On a balmy afternoon in the Rheinland, die Nullfünfer made the far more assured start, and seized the initiative just five minutes in.
Pablo De Blasis – a thorn in the Magpies’ side throughout – split the backline in two with a superb threaded pass, and German Under-21 international Levin Öztunali side-footed the ball into the far corner.
United took their time to get going at the Opel Arena but, midway through the first half, they came close twice in quick succession.
Mohamed Diamé picked out Siem de Jong’s run with a floated ball over the top, which the Dutchman did well to take down. He managed to get a shot away, too, but René Adler narrowed the angle and produced a fine block.
A couple of minutes later, Paul Dummett – handed the armband by Rafa Benítez – crossed for Aleksandar Mitrović ten yards out, whose headed effort dropped off-target.
Again, though, Mainz upped the ante, and came close to extending their lead on a string of occasions before the break.
With 25 minutes on the clock, Alexandru Maxim’s mis-hit shot fell kindly for Stefan Bell deep inside the penalty area but, with more time than realised, the hosts’ skipper sent the ball rolling harmlessly wide.
Another fine move saw Danny Latza and Yoshinori Muto link up for die Nullfünfer, before the latter teed up Maxim 20 yards from goal. The Romanian took a touch to set himself but Jack Colback got in the way of his right-footed strike.
Just before the interval, De Blasis pounced on a loose ball deep on the left but failed to keep his low-struck drive on target.
The home side started the second half as they ended the first. Just minutes in, Maxim’s corner dropped for Daniel Brosinski on the edge of the penalty area, whose sweetly-struck volley bounced agonisingly wide with Karl Darlow beaten.
Brosinski then tested Darlow from distance again, before Fabian Frei’s 20-yard effort slithered past the post.
Dwight Gayle, Ayozé Perez and Jonjo Shelvey were among those to enter the fray for United just after the hour-mark but, five minutes later, their equaliser arrived from a far more unlikely source.
Christian Atsu – another substitute – got the better of his man before whipping in a fine cross from the right, which was only cleared as far as Gámez. Die Nullfünfer’s replacement ‘keeper, Robin Zentner, looked to have the Spaniard’s effort covered, but an almighty deflection carried it across the line.
With 20 minutes remaining, Mainz almost re-took the lead through Fischer, but Freddie Woodman – not long on for Darlow – produced a superb low stop.
At the other end, a loose ball looked to have trickled out nicely for Pérez – celebrating his 24th birthday – but the Spaniard blazed over the top.
Pérez then glanced an Atsu cross just off-target, but any hopes United had of completing the turnaround were dashed five minutes from time.
Suat Serdar checked inside and slid in a low cross for Fischer, who swept the ball beyond a helpless Woodman and into the far corner.