Ahead of the game, AGF coach Jakob Poulsen had identified getting an early goal as the key to staging an unlikely comeback after the 1-4 defeat in Randers a fortnight ago.
And they nearly got exactly what they wanted after 14 minutes when Frederik Emmery searched down the wing and produced a perfect delivery for Kristian Arnstad, whose effort unfortunately hit Tobias Bech and went out for a goal kick.
Mikael Ishak scored the first goal for Lech Poznan in the first leg, and the Swedish striker nearly repeated that feat when he rose high to produce a strong header towards goal, but Mads Hedenstad diverted the effort over the crossbar.
A minute later, the home side thought they had won a penalty when Jonas Jensen-Abbew at first was adjudged by the referee to have handled the ball in the box, but following a VAR review, the decision was changed.
Then, after 32 minutes, the visitors were rewarded for their ball possession when Tobias Bech took advantage of great work by Arnstad to fire the ball into the roof of the net via a deflection.
Lech Poznan seemed to come out with more purpose after the restart, but still the Danish visitors managed to double their lead nine minutes after the interval, when AGF were awarded a penalty after Robert Gumny had handled a delivery from Emmery. Arnstad converted the penalty even though Poznan keeper Mateusz Lis got a touch to it.
Then, with 15 minutes to go, Fredrik Tingager headed home a corner from Erik Karl to force the game into extra time. In extra-time, the home side seemed to regain the momentum, when Filip Jagiello coolly slotted the ball into the net from a rebound after 95 minutes. But the Danes refused to surrender and restored parity on aggregate when Tomas Kristjansson restored the three-goal lead five minutes later.
In the penalty shoot-out, the Danish visitors had the better nerves, scoring four out of five attempts, while goalkeeper Mads Hedenstad saved two attempts.