Alan Dzagoev headed in Andrei Arshavin's 37th-minute free-kick to put Russia ahead in the Group A clash at Warsaw's National Stadium.
However, Blaszczykowski's strike from outside the box after an assist from his Borussia Dortmund team-mate Lukas Piszczek in the 57th minute earned Poland another vital point.
Ugly scenes on the streets of Warsaw prior to kick-off threatened to overshadow this keenly-anticipated match, but both teams turned the focus back to football with a thrilling end-to-end tussle.
Blaszczykowski's goal scuppered Russia's hopes of becoming the first team to book their place in the knockout stages.
It was a richly-deserved point for the Poles, who were frustrated in their opening draw with Greece, but set a stunning pace in the first period and repelled the majority of the impressive Russian advances.
Franciszek Smuda's side almost grabbed a seventh-minute lead when a glancing header from Sebastian Boenisch was superbly saved by Russian keeper Vyacheslav Malafeev, who was kept busy throughout the night.
Boenisch rose highest again from the resulting corner but this time could only direct his header into the arms of a relieved Malafeev.
With the Russians struggling to make any kind of impact, Poland continued to press and Robert Lewandowski almost conjured an opener out of nothing when he hooked a volley just over the bar in the 12th minute.
Poland had the ball in the net in the 19th minute when Lewandowski played in Eugen Polanski who drilled a low shot beyond Malafeev but was correctly pulled up for straying offside.
Playing an exciting brand of fluent passing football, the Poles were dominant and Russian defender Sergei Ignashevich had to get in with a fine intervention to deny Lewandowski another chance in the box.
Russia finally started to get to grips with the game as it approached the half-hour mark, with first Arshavin bursting down the right and crossing for Alexander Kerzhakov, who headed high and wide.
And in the 28th minute, the roles were reversed as Kerzhakov turned provider from the right, sending in a low cross which just eluded the stretching Arshavin in front of goal.
Russia's best spell of the match resulted in the opening goal in the 37th minute as Arshavin delivered a superb free-kick from the left flank and Dzagoev flashed home a header past Przemyslaw Tyton.
Poland almost responded immediately, with Blaszczykowski's powerful drive beaten away by Malafeev, but the Russians were beginning to play with the same kind of confident swagger evident in their opening group win.
But Russia ended the half well on top, with Dzagoev and Yuri Zhirkov both having close-range chances and the goalscorer unlucky not to earn a penalty in first-half injury-time after being pushed over in the box.
Poland started the second half in the same manner they approached the first, and came close within two minutes of the restart when Polanski's brilliant through-ball found Lewandowski but he was pushed wide and out of play by the advancing Malafeev.
It was all Poland again with Ludovic Obraniak and Damien Perquis both coming close before the Russians threatened with a swift counter in the 50th minute, Kerzhakov's dangerous run eventually intercepted by Dariusz Dudka.
Blaszczykowski sparked jubilation in the 58th minute when he got on the end of a Polish breakaway down the right and cut inside to sent a superb left-foot drive beyond Malafeev and into the corner of the net.
As the game sprang into life, Dzagoev scuffed a shot straight at Tyton after being flicked through by Kerzhakov, and almost immediately at the other end Blaszczykowski made ground down the left before blazing high and wide.
The result means Russia top Group A with four points, with the Czech Republic second after they beat Greece 2-1 in Wroclaw earlier in the day. Poland are third with two points, and the Greeks are bottom with one point.
The group concludes on Saturday night, when Russia face Greece and Poland take on Czech Republic knowing they must win to have any chance of progressing to the quarter-finals.