The match was marred before kickoff by fighting between hooligans from both countries, leaving several people injured as thousands of Russian fans marched to celebrate the Russia Day national holiday.
Dzagoev darted past defender Lukasz Piszczek in the 37th minute and sent a glancing header beyond goalkeeper Przemyslaw Tyton after a curling free kick from Andrei Arshavin.
But Poland was rewarded for its attacking intent in the 57th when Blaszczykowski cut in from the right and sent a searing left-foot drive into the far corner of the goal.
The result left Russia at the top of Group A with four points but also kept alive Poland's chances of qualifying for the quarterfinals.
Russia's rampant attack in the opening 4-1 win over the Czech Republic was largely muzzled by a well-organized Polish defence. At the other end, Robert Lewandowski was a constant threat.
Earlier Tuesday, the Czechs played themselves back into Group A contention by scoring two early goals and hanging on to beat Greece 2-1, meaning all four teams can still qualify.
As it did in its opening 1-1 draw with Greece, Poland started strongly, but this time had to wait nearly an hour before finally converting a chance.
Eugen Polanski thought he had put Poland ahead in the 18th minute after he rounded off a slick passing move by shooting past Vyacheslav Malafeev, but his effort was ruled offside.
Despite the Polish pressure, Russia remained dangerous at the other end and gradually began to assert itself as the first half wore on.
Tyton rushed off his line and dived at Aleksandr Kerzhakov's feet to deny the Russia forward a shooting chance in the 10th minute. Kerzhakov then headed wide after a cross from Arshavin, and the attacking pair switched roles two minutes later when Arshavin barely failed to get on the end of a cross from the right.
But Poland again started strongly in the second half as Lewandowski ran into the penalty area, but Malafeev forced him wide and blocked his shot with his legs. Lewandowski came close again when he nearly connected to a cross from Obraniak, but Malafeev again beat him to the ball.
Poland coach Franciszek Smuda tried to press home the advantage by replacing defensive midfielder Dariusz Dudka with more attack-minded Adrian Mierzejewski in the 73rd minute, but the Russia defence held firm.Suggest a correction