Parisse was instrumental in at least three of Italy's six first-half tries, scoring the first and setting up two others as the clinical Italians dominated the forward exchanges to notch 50 points for the first time in a World Cup match.
"We are very happy to take the victory and the five points which was very important for us to try and qualify (for the quarter-finals)," Parisse said in a pitch-side interview.
"We scored some tries and we take confidence in our attack but our defence must improve because the U.S.A. and Ireland will be very hard," he added of their final two pool opponents.
Winger Giulio Toniolatti and centre Tommaso Benvenuti also scored two tries each, while scrumhalf Edoardo Gori, winger Luke McLean and Alessandro Zanni also crossed for the Italians.
Italy coach Nick Mallett said his team got off to a good start but lost their way a bit.
"I was very happy with the way we started the first half but then we got a bit loose. Russia ran hard at us, kept the ball and played some nice rugby," he said.
"We needed five points to make sure we go into the game against Ireland with a good shot at going through."
The Italian scrum, which constantly had the Russians on the back foot, was also rewarded when referee Waynes Barnes gave a penalty try after the Russians had collaped the scrum for the fourth time on their goal line.
Flyhalf Riccardo Bocchino converted four of their first half tries, though he and Benvenuti missed five conversions between them.
Italy hooker Fabio Ongaro was sin-binned for an illegal tackle on Igor Klyuchnikov when he went into the tackle without wrapping his arms around the Russian fullback.
Russia took full advantage when replacement scrumhalf Alexander Yanyushkin darted over for his side's first try at the World Cup and flyhalf Konstantin Rachkov converted from wide.
Russian captain Vladislav Korshunov was pleased his side had managed to score tries but thought the defence could have been tighter.
"I am glad we scored so many tries, it was the first for Russia at a World Cup, but we are disappointed to give away so many tries," he added.
"We were competitive but every game is a new step for us and hopefully we will score more tries and concede less in the next game."
Benvenuti gabbed his second try of the game when he kicked ahead and won the race to the ball to give the Italians a 43-7 lead shortly after the halftime break, before Russian Vladimir Ostroushko scored his side's second try after a sustained buildup.
Italy winger McLean, who had been a constant threat, crossed for his side's eighth try before Russia centre Alexei Makovetsky took a long pass on the left and went over for Russia's third.
Replacement loose forward Alessandro Zanni barged over for Italy's ninth and final try.
"Our play was not so good tonight but I am glad we scored some tries, they are the first tries for the Russian team at the tournament," Russian lock Alexander Voitov said.
"It's a tough game and each game is new for us and we are very glad to be here."