The home side made a sloppy start and consequently trailed to world No.20 Russia and Kirill Golosnitskiy's converted try for much of the opening period in Tokyo.
But Matsushima, having already reduced the arrears, edged Japan in front just before the half-time whistle and set up a far more straightforward second period.
Pieter Labuschagne went alone for a powerful third try and then Matsushima secured a potentially precious bonus point, becoming the first Japanese player to score a Rugby World Cup treble.
A long way from the procession that would follow, the nervy Brave Blossoms had been punished inside five minutes as William Tupou completely misjudged Vasily Artemyev's high kick and allowed Golosnitskiy to steal in for the opening try.
But the hosts kept their cool and responded in fine fashion, with Timothy Lafaele and Yutaka Nagare combining stylishly to open up space for Matsushima to dart through on the right.
It looked as though Russia might get to the break with a narrow lead still intact when Matsushima saw a second try struck off, having lost control of the ball as he lunged for the line under a tackle from Artemyev.
However, the Japan finisher made no mistake on the stroke of half-time, being found wide open to sprint in for a vital score.
Yu Tamura dispatched a simple penalty shortly after the restart to stretch Japan's advantage, before a brutal Labuschagne try as he ripped the ball from Andrey Ostrikov and streaked clear.
A gutsy Russia display was rewarded with three points from the boot of Yury Kushnarev, but Tamura hit back with a penalty of his own and Matsushima slalomed through to wrap up victory after Artemyev gifted away a tired kick.
Having successfully negotiated this potential banana skin, Japan has a week off before returning to its traditional role as underdog for a highly anticipated clash with Ireland. Russia faces Samoa next.