Yeremy Pino drew the sides level six minutes after the restart and Mateta – who had a first-half goal chalked off by VAR – fired Palace to a first-time lead four minutes later.
Junior Olaitan netted a 73rd-minute equaliser, and Palace could not complete a second comeback after Umit Akdag was sent off for a clumsy 77th-minute challenge on Jorgen Strand Larsen, who was subsequently forced off.
There were sweeping changes for the hosts from Monday’s defeat to Trabzonspor as Vincenzo Italiano introduced nine different starters.
Mateta thought he had scored his first goal since the Conference League winner in May until a VAR check deemed him to be marginally offside in the build-up.
Still, it was a promising start for Palace, who had won the ball through determined pressing.
The visitors kept the pressure on, and there was another good chance when Yeremy Pino found Adam Wharton with a neat flick, but the England midfielder’s delivery to Mateta skipped past the striker.
Palace had limited the hosts to just Oh Hyeon-gyu’s nodded attempt as the contest ticked past 20 minutes and Tyrick Mitchell dragged an effort wide, though he might have wanted to pick out the approaching Mateta.
Mateta forced Alexander Nubel into a save from Wharton’s corner just before the half hour, and nodded another one wide soon after from their third corner of the night.
Palace fell behind in added time before the break, when they let the hosts take advantage of a gap between their centre-backs and failed to spot the run of Ndidi, who latched onto Yasin Ozcan’s long ball and slotted the opener into the bottom corner with his left foot.
The Eagles squared it up after the restart, the product of some good work by Dwight McNeil and Anan Khalaili to find Pino, who swept it home on the slide.
The equaliser was originally chalked off for offside, but the call was reversed following a VAR check.
They took the lead five minutes later, this time capitalising on a Besiktas error Mateta was quick to read, inspiring him to take off running, ultimately punishing the hosts when he blasted into the roof of the net.
Mateta was replaced by Strand Larsen just after the hour in a double swap which also saw Ismaila Sarr replace McNeil.
Olaitan then drew the sides back level, making quick work of the Palace defence before firing past the diving Benitez.
The Turkish side went down to 10 men with 13 minutes remaining following Akdag’s clumsy challenge on Strand Larsen, and a Palace penalty shout moments later was dismissed.
Strand Larsen was forced off, in obvious pain off the ball, and hobbled off with his arm around a staff member, and replaced by Eddie Nketiah, who fired into the side-netting with his first chance from an awkward angle.
The hosts stood firm, and closed out the contest before the Eagles could inflict any more damage.