Kenan Karaman slotted in a stoppage-time equaliser after Luca Waldschmidt fired in an 81st-minute volley that had put Germany 3-2 ahead.
Turkey twice before had levelled, with both teams missing several regular players.
"We have to be more dominant. It is disappointing because at the end it is about winning and we did not succeed."
Germany also went ahead in their last two matches against Spain and Switzerland in September but both times had to settle for a draw.
Draxler's good finish from a Kai Havertz assist had put the hosts ahead on the stroke of halftime in front of 300 fans allowed in the stadium but the Turks equalised with Ozan Tufan's curled effort five minutes after the restart.
The 23-year-old Neuhaus completed a lightning quick one-two with Havertz to put Germany back ahead in the 58th.
The Germans, playing without Bayern Munich and RB Leipzig players who were rested and missing several more through illness and injury, face Ukraine on Saturday and Switzerland three days later in the Nations League.
Turkey play Russia on Sunday and Serbia next Wednesday in their Nations League matches.