The Poles, needing to take at least a point from the Group A match in the wake of their 1-1 tournament opener against Greece on Friday, were keenly aware of Russia's high-octane 4-1 performance against the Czech Republic the same night.
A goal by Alan Dzagoev in the first-half - his third of the tournament - was cancelled out in spectacular fashion in the second-half by Polish captain Kuba Blaszczykowski.
Dutch coach Dick Advocaat praised Poland for their performance but added he was happy with the point.
"Poland played very well tonight being under the risk of losing the chance to win a place in the last eight if they lost," he said.
"Meanwhile, we allowed them to create too many chances in attack.
"That means we still need to strengthen our defence. We also played well and scored before the break and had many chances in the second but we missed them all. In general, I'd say the draw is a good result for us," said the 64-year-old Dutchman.
Russian captain Andrei Arshavin said that while the point was welcome they only had themselves to blame for allowing the Poles back into the game.
"We started well and took the lead but after the break we played too loosely allowing Poland to reply on dangerous counter-attacks," he said.
Poland coach Franciszek Smuda was happy with the result but above all with the way his players had stuck to their gameplan - he won't be so happy with the angry manner in which Ludovic Obraniak shrugged him aside on being taken off in the final minute.
"We are a young side, and we are going to get ever better.
"I am above all happy with the players because they played to the gameplan from the first to last minute."
In what may be the most politically-charged fixture of the tournament, Poland looked the hungrier team in the first half, launching a series of convincing attacks on the Russian goal.
Hard work appeared to have paid off when Eugen Polanski moved onto a through ball from lone striker Robert Lewandowski and fired past Vyacheslav Malafeev.
But fans and the Polish bench swung from ecstasy to misery when his 18th-minute shot was ruled offside.
A resurgent Russia picked up the pace, with Arshavin crossing in the 25th minute to Aleksandr Kerzhakov, only for him to miss the target.
Polish keeper Przeymslaw Tyton - whose penalty-saving heroics after he came on as a substitute for red-carded first choice Wojciech Szczesny helped avoid a Polish defeat to Greece - saved a free kick from Arshavin a minute later.
Russia's efforts bore fruit in the 37th minute when rising star Dzagoev, who notched a double against the Czechs, latched onto an inswinging Arshavin free kick to open the scoring.
The Poles appeared tired, but battled hard, and finally equalised in the 57th minute when Blaszczykowski picked up a cross from Obraniak and fired home a left-footed piledriver.
There were nervous moments for both sides in the remainder of the half, with the noise levels rising in Warsaw's brand-new National Stadium.
Sporting encounters between Poland and Russia are often high pressure, as they feed into centuries of antipathy between the two nations, and the rivalry in the stadium's terraces was palpable from the start of the match.
Tensions had risen in Warsaw beforehand, as police made dozens of arrests and used water canons to halt brawls between fans from both camps.
With the Czech Republic having beaten Greece 2-1 earlier on Tuesday, Russia top Group A on four points after two matches with the Czechs second on three points, Poland third on two and Greece fourth on one.
Russia wrap up their group matches against Greece on Saturday, when Poland face the Czechs.