The striker, Crystal Palace’s top scorer this term with 11 goals, scored twice in the space of four first-half minutes to give the Red Devils a 3-1 lead at half-time.
Everton winger Kevin Mirallas had earlier equalised after Viktor Vasin’s third-minute opener for the hosts.
Aleksey Miranchuk halved the deficit for Russia in the 74th minute before Aleksandr Bukharov scored the equaliser in injury time.
After winning his first four matches in charge of Belgium, manager Roberto Martinez has seen his side draw their last two games.
They required a late goal from Romelu Lukaku to rescue a point in Saturday’s World Cup qualifier against Greece in Brussels.
Kostas Mitroglou had given Greece the lead but Everton striker Lukaku struck two minutes from time to save Belgium’s blushes.