Smuda's can still advance to the quarter-finals after the Dortmund man cancelled out Dzagoev's first-half effort with a beautiful strikeJakub Blaszczykowski's spectacular strike helped Poland secure a 1-1 draw against Russia in Group A action on Tuesday, which leaves all four teams with a chance of qualifying for the last eight.
The co-hosts had some excellent chances in the first-half but found themselves 1-0 down at the break. Alan Dzagoev netted his third goal of the tournament when he diverted Andrey Arshavin's precise free-kick beyond Przemyslaw Tyton.
The goal gave the Russian's confidence but they were dragged back by Blaszczykowski's magic after a lethal counterattack from the Poles sent the home fans into ecstasy.
Russia showed greater composure early on with Arshavin continuing his fine form. Urged on by their supporters, however, Poland got a foothold in the game and fashioned the first opportunity.
Ludovic Obraniak swung an inviting free-kick into the area which Sebastian Boenisch was on the end of, but the Bremen man was denied by Vyacheslav Malafeev whose sprawling legs kept the score level.
Poland continued to pour it on and Robert Lewandowski looked to add to his Euro 2012 tally with the opening strike. The Dortmund striker, full of confidence, took the ball down before unleashing a volley towards goal that was narrowly off target.
In response Dick Advocaat's side looked to thread the ball through a static Polish defence and Aleksandr Kerzhakov thought he had won a penalty when Damien Perquis slid in from behind but the defender had expertly clipped the ball away from the Zenit striker.
The noise levels increased ten-fold when Eugen Polanski finished a beautiful flowing move from the co-hosts only for his celebrations to be cut short when he noticed that he had correctly been judged offside.
Franciszek Smuda's side continued to create chances as Marcin Wasilewski drove in a low cross only for the ball to squirm away from both Lewandowski and Blaszczykowski with the goal beckoning.
Replicating the driven cross from Wasilweski, Kerzhakov delivered the same for Russia only to see the ball flash across the face of the goal with no decisive touch.
With the visitors enjoying their best spell of the game they took the lead when Dzagoev flicked home his third goal of the tournament. Arshavin's perfectly flighted free-kick found the youngster unmarked and he provided the touch that sent the Russia fans into raptures.
Poland looked to find an equaliser in the remaining eight minutes of the half and Malafeev had to be alert to palm away Blaszczykowski's drive.
And the home side started the second half in attacking mode as Polanski looked to the slide the ball through to Lewandowski but the pass was too heavy and the striker had to settle for a corner kick.
Poland continued to probe and launched a superb counterattack which ended when Obraniak's delicious cross was punched clear by Malafeev with Lewandowski's boot close by.
Russia suddenly found their attacking desire as Arshavin rode a challenge to burst forward before wasting a glorious opportunity misplacing his pass with Russia a man up on the attack.
And seconds later Poland launched their own counter as Lukasz Piszczek looked to link-up with his club team-mate. The full-back found Blaszczykowski with a wonderful pass, and the Dortmund man's first-touch was simply sublime before unleashing a vicious left-footed shot which caused Warsaw to erupt as it flashed past Malafeev to bring Poland level.
The atmosphere in the stadium intensified and Malafeev was called upon yet again for the Russians as Poland searched for a second. The keeper stood tall at his near post to deny Polanski's low shot that had been hit with some conviction albeit from a tight angle.
As the value of a winner increased as each minute passed neither side was able to find a telling moment in the final exchanges.
The result leaves Russia at the summit of Group A with four points, while the co-hosts are third with two after Czech Republic defeated Greece.
Poland will need to win their final game to progress, while Russia need a point against Greece to secure a quarter-final birth.