Russia playmaker Alan Dzagoev put the hosts ahead with a nicely-taken free-kick from the edge of the box 10 minutes into the second half.
Italian Capello, who replaced Dutchman Dick Advocaat as Russia boss last month, gave defender Georgy Shennikov and midfielder Viktor Faizulin their national team debuts while leaving under-fire captain Andrei Arshavin on the sidelines in the first half.
Capello's strategy paid off as the home team dominated before Dzagoev, Euro 2012 joint top scorer with three goals, gave the Russians a deserved lead on 55 minutes.
The Ivorians, missing six players through injury, were content to play safe in the first half.
They also missed Arsenal striker Gervinho and West Ham United defender Guy Demel because they did not get permission from their English clubs to travel to Russia.
The visitors increased the tempo after falling behind and midfielder Abdul Razack wasted a good chance midway through the second half when he struck the post from close range after a nice feed by Didier Drogba.
Soon after, Gradel headed against the crossbar but followed his own rebound to fire into an empty goal 13 minutes from time with keeper Vyacheslav Malafeev unable to get off the ground after reacting to the initial shot.
Capello, who was seen grimacing on the bench as the ball trickled into Russia's goal, was nevertheless satisfied with the final outcome.
"It was a tough game but I'm pleased the way we played," the former England manager told reporters. "It was a good test for several young players, making their national team debuts."
Capello brought Arshavin into the game midway through the second half but the forward, who was greeted by a chorus of whistles and boos from the home crowd, looked out of pace.
"I was unpleasantly surprised to see fans whistling Arshavin. I just don't understand that," Capello said. "We lost concentration because of that and soon conceded a goal."
Arshavin, seen by fans and local media as one of the main culprits for Russia's Euro 2012 flop, added: "Of course I was disappointed by the fans' reaction but I tried to ignore it the best I could."
The Russians also lost Alexander Anyukov to injury in the first half, the right-back suffering a concussion after colliding with two opponents in mid-air.
The game was Capello's only test before Russia host Northern Ireland in a 2014 World Cup qualifier on September 7, while Ivory Coast resume their World Cup qualifying campaign against Gambia next March.
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