Benteke led the Belgian line, while Youri Tielemans was handed a spot in midfield as head coach Roberto Martinez shuffled his pack following their 1-1 draw with Greece in last week's 2018 World Cup qualification fixture.
Russia started the brighter, but it was Belgium that created the better opportunities in the first period, and the visitors took the lead in the 43rd minute when Benteke headed home from close range after Jan Vertonghen had seen his own effort blocked.
It then went from bad to worse for Russia two minutes later when Benteke scored his second of the night with a well-placed header from a Nacer Chadli free kick to leave Belgium with a 3-1 lead at the half-time break.
Toby Alderweireld might have scored a fourth for Belgium early in the second period after lacklustre defending from Russia presented the Tottenham Hotspur centre-back with a shooting chance, but his low effort was wide of the post.
Aleksandr Bukharov thought that he had cut the deficit to one goal 20 minutes from time when he converted from close range, but the 32-year-old forward was flagged offside as Russia's frustrations continued.
The hosts did have their second in the 74th minute, however, when Aleksey Miranchuk, who had been on the field less than two minutes, converted after smart work from Bukharov.
Russia then scored their third of the night in the second minute of additional time at the end of the 90 when Bukharov found the bottom corner with a powerful effort to ensure that his team avoided defeat on home soil.