The co-hosts came from behind during a thrilling second half, captain Jakub Blaszczykowski scoring the equaliser with a thunderous left-foot shot.
Russia had taken the lead after 37 minutes, when Alan Dzagoev turned in Andrey Arshavin's curling free-kick.
Although both teams had chances to win the game, the spoils were shared.
The result leaves Group A wide open, with all four teams still mathematically able to qualify for the quarter-finals after a night of high drama in the Polish capital.
This was not a rivalry in need of stoking, or a fixture that required additional hype.
And yet fuel was thrown on the fire in the hours before kick-off as riot police clashed with fans from both countries in a series of violent exchanges on the streets of Warsaw.
A march in support of Russia's Independence Day, from the city centre to the stadium, prompted widespread anger among Polish extremists.
If the atmosphere around the stadium was raw at kick-off, the early exchanges were equally frenzied.
Arshavin was immediately in the thick of the action, probing, pressing, jinking beyond defenders. But the best of the early chances fell to Poland.
Ludovic Obraniak's curling free-kick was headed goalwards by Sebastian Boenisch only for Russia goalkeeper Vyacheslav Malafeev to turn the ball away.
Poland had the ball in the net after 17 minutes, but the linesman's flag correctly denied them after Robert Lewandowski and Eugen Polanski had linked up delightfully following an incisive one-touch passing move.