The former Nigerian international came face to face with his former Super Eagles teammates Wilfred Ndidi and Kelechi Iheanacho who were also on parade for Leicester City.
After a goalless first half, Moses succeeded in putting the Russians ahead with a fine diving header on the 51st minute with a header.
The former Chelsea forward who also assisted two goals in the first meeting last week has now been involved in four goals in four Europa League games for Spartak Moscow this season.
However, the lead lasted for just seven minutes as Ghanaian defender Daniel Amartey restored parity for the home with a header from a corner kick.
Moses then gave away penalty after fouling Ademola Lookman in the box, but veteran striker Jamie Vardy failed to covert from the spot.
Both sides failed to find the winner and they are at the risk of missing out of the next round tickets.