Matsushima touched down for three tries, making history as the first Japanese player to do so in a World Cup game, to ensure victory.
It was a horrible start for the nervy Cherry Blossoms after they fumbled the kick-off.
After just five minutes Russia took the lead when Kirill Golosnitskiy pounced on a Japanese knock-on, broke through a tackle and scored.
The hosts were shell-shocked at 7-0 down.
But they hit back seven minutes later when Matsushima got his first try of the night after a lovely offload.
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Russia continued to stifle Japan with their line speed and kicking game.
The Brave Blossoms struggled to deal with high kicks and made many errors.
Right before the half-time break Matsushima got over the try-line again, but the five-pointer was chalked off by the video referee after he lost control of the ball.
The winger made amends just before the interval, putting the hosts 12-7 ahead.
In the second half Japan took a 15-7 lead through a penalty goal.
With the Russians tiring against their speedy opponents, the Brave Blossoms looked to take advantage.
Japan started to keep the ball in tight and make Russia work harder in defence.
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A brilliant solo try then came to Pieter Labuschagne when he ripped the ball free and raced away 50 metres to touch down.
Japan appeared in control at 20-7.
But Russia kept coming and after winning a series of scrum penalties, they nailed a shot at goal to make it 20-10.
The two teams traded penalty goals, Japan going to 23-10, before Matsushima struck for the third and final time.
A poor Russian kick was punished with a quick shift to the right and the winger glided over.
Japan escaped as winners, but Russia leave Tokyo with a lot of respect for their hardy display.