Direct proof of use
Moskva's use in the 2011 Syrian Civil War is documented as deployment and fielding with Russia's naval force supporting the pro-government intervention, not as a land-attack missile firing. USNI News reported on 5 October 2015 that a Russian surface action group led by the Moskva missile cruiser was in the eastern Mediterranean and was likely there to provide an air-defense bubble for Russian fighters striking targets in Syria.
RUSI identified the Slava-class / Project 1164 Moskva missile cruiser, hull number 121, as part of the Russian naval squadron operating near the Syrian coast as of 8 November 2015. RUSI described the naval force's role as deterring potential Western interference and providing long-range air-defense coverage against a no-fly zone over northern Syria, with Moskva's S-300F Fort battery serving that air-defense purpose.
Sources: USNI Russian Warships Protect Strike Fighters, RUSI Detailing Russian Forces in Syria
Timeline
The documented sequence begins with Russia's September 2015 air intervention from the Latakia area and contemporaneous reporting that Black Sea Fleet surface combatants had moved into the eastern Mediterranean. By early October, USNI News connected the surface group led by Moskva to protection of Russian strike aircraft operating from Syria.
RUSI's November 2015 force survey then placed Moskva in the Russian naval squadron near Syria and explained its role inside the wider Russian Expeditionary Corps. The sources support a naval air-defense and force-protection role, while they do not document Moskva firing missiles at Syrian battlefield targets.
Sources: USNI Russian Warships Protect Strike Fighters, RUSI Detailing Russian Forces in Syria
Narrative
Moskva's Syrian Civil War role was maritime cover for Russia's intervention on the Syrian government's side. The cruiser brought a large surface combatant, command presence, anti-ship armament, and an S-300F Fort area-air-defense battery to the eastern Mediterranean at the same time Russian aircraft were flying from the Latakia area.
The most specific supported function was air defense. USNI News described the surface action group as protection for Russian strike fighters, while RUSI stated that Moskva's S-300F Fort battery served the long-range air-defense role for the naval force and Russian operation. This made the cruiser part of Russia's protective and deterrent posture around the air campaign rather than a documented strike platform in Syria.
Sources: USNI Russian Warships Protect Strike Fighters, RUSI Detailing Russian Forces in Syria