Police said they had detained almost 60 unruly fans on both sides while about seven were treated for minor injuries ahead of a match that the authorities say is posing the city's "greatest ever" security challenge.
Tensions have been stoked by centuries of bad blood and suspicion between the two countries, coupled with pockets of fans on both sides with a reputation for violence.
Police sprayed water cannon on Polish fans near the stadium before the kickoff while tear gas was used in another area near the venue which was encircled by a thick cordon of riot police with dogs and rubber-bullet guns.
Riot police and vans created a buffer as Russian fans began marching to the National Stadium across a central Warsaw bridge chanting "Russia, Russia" and waving white, blue and red Russian flags.
Some Polish fans yelled verbal abuse at the Russian marchers, who responded by hurling back bottles, but security forces swiftly managed to keep the situation in check on what is also Russia's national day.
Helicopters circled the city sky as vuvuzelas blared below and thousands of chanting Poland fans decked out in their national red-and-white also made their way in a loud but orderly fashion to the stadium.
Some 6,000 policemen are on duty in the capital for the duration of the tournament and Poland's Euro 2012 organisers have said that 9,800 Russian and 29,300 Polish fans had tickets for Tuesday's encounter.
Some 12,000 Russian fans are in the city for match day.
Interior Minister Jacek Cichocki confirmed a heavier police presence in Warsaw after dubbing the security operation the city's "greatest-ever challenge".
"Drunk fans both in the city centre and on the outskirts of Warsaw after the game -- especially around midnight -- that's a real concern to us," added Prime Minister Donald Tusk.
Tusk also hit back at claims of racism levelled at Poland, with a number of reported incidents, most notably taunts at members of the Dutch national team as they trained in Krakow.
Russian fans are also alleged to have taunted Ethiopian-Czech player Theodor Gebre Selassie.
"Let's be honest, racist and anti-Semitic attitudes among Polish hooligans are a fact. But I strongly protest against stigmatising Poland as a country in which this phenomenon is growing," he said.
Some Russian fans insisted the security issue was overblown.
"We won't be provoking anything," said Svetoslaw Sorokine, 33, who travelled 48 hours by train from Yoshkar-Ola, a city 800 kilometres (500 miles) east of Moscow, for the match.
"Our supporters come in a spirit of peace to support our team, not to play politics," he added.
Fellow fan Ilya Koulikov, a Moscow native, said fears of clashes among fans were being "fuelled by the media who are stoking the fire. People have come for the football."
Polish media played up the tense history of the old foes, with the centre-left daily Gazeta Wyborcza resorting to military language.
"It won't be a simple march across Warsaw, alas, but massive air raids against the Polish net," the newspaper said. "Above all, we must survive this match."
Russia come into the game on a high after thumping the Czech Republic 4-1 in their first game, but Poland drew 1-1 with Greece, making a win a must for the Euro 2012 co-hosts if they are to go through to the last eight.
Football-mad Tusk joked that his "trembling heart" predicted a 4-0 victory for Poland but "reason and my football savvy tell me it's going to a very tough match."
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