Police said they had detained nearly 130 unruly fans on both sides while about 10 were treated for minor injuries before the match, which the authorities said posed the city's "greatest ever" security challenge.
Tension was 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.
But the 1-1 result appeared to have eased the post-match mood, with no major incidents reported after midnight (2200 GMT), as Poles celebrated their chance to advance in the 16-nation quadrennial tournament they are co-hosting with Ukraine.
Earlier, police sprayed water cannon at Polish fans near the stadium before the kick-off 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 national flags on what was also their national day.
Rubber bullets and pepper spray were also part of the anti-brawl arsenal authorities used to douse brawls, local media reported.
Some Polish fans yelled obscenities at the Russian marchers, who responded by hurling back bottles, but security forces swiftly managed to keep the situation in check.
Helicopters circled the city sky, as "vuvuzela" trumpets 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 police 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 were in the city for match day.
Before kick-off, Russia's national anthem was met with jeers and whistles as the country's supporters unfurled a giant flag emblazoned with a sword-wielding warrior and the words "This is Russia" from their enclosure in the stands.
Poland's Interior Minister Jacek Cichocki had earlier said the security operation surrounding the match in the capital was the city's "greatest-ever challenge", as Polish newspapers played up the match with military language and historical references.
Prime Minister Donald Tusk warned that drunken fans after the game were "a real concern".
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.
European football's governing body UEFA is also looking into allegations that Russian fans 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.
Before the match 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."