Russia could not regain their lead, making it seven matches without a win heading into their World Cup opener against Saudi Arabia, while Turkey are now unbeaten in five - each of those coming in friendlies.
Turkey had been on top at that point and soon tightened their grip on proceedings, without being able to damage the home side.
Neither side could muster a serious effort on target prior to the breakthrough moment, which arrived 10 minutes before the interval.
Russia looked the better side in the build-up to half time, but Turkey created the next clear-cut opening for Kenan Karaman to head straight at Akinfeev.
Turkey, who are due to face Russia in a couple of competitive matches later this year in the UEFA Nations League, made a few changes at the break in an attempt to freshen things up, including the introduction of Malli.
The score was levelled up on the hour mark thanks to some poor Russian defending, with Malli getting on the end of Kirintili's punt upfield and guiding the ball out of Akinfeev's reach from the edge of the area.
Russia, whose last win came back in October, almost regained their lead soon after when Golovin's effort deflected past Kirintili's post for a corner.
Golovin would have an even better chance 15 minutes from time, taking down a ball over the top and cutting inside his man before bending it wide.
Turkey themselves had an opportunity to win the match, though, as Malli was picked out in a good position but could not keep his shot on target.
The flow of the game was not helped in the second half by the flurry of subs, and that Malli shot would prove to be the last serious chance of the contest.
RUSSIA (3-5-2): Akinfeev; Smolnikov (Fernandes 77'), Ignasevich, Kutepov; Zhirkov, Zobnin (Kuzyayev 94'), Golovin, Gazinskiy (Kudryashov 76'), Samedov; Dzagoev (Miranchuk 60'), Smolov
TURKEY (4-3-3): Serkan; Ozbayrakli (Celik 90'), Ayhan, Soyuncu, Kaldirim; Kahveci (Malli 46'), Yokuslu, Tekdemir (Topal 46'); Yazici (Ozyakup 46'), Karaman (Akbabar 82'), Cengiz Under (Gurler 76')