The Polish win was deserved and could have been by a bigger margin, but the visitors wasted two big opportunities in the second half.
Silkeborg have had a terrible start to the season in the Superliga, where the team has lost three games without scoring a single goal.
However, this was not evident from the beginning of Thursday's match on the artificial turf in Silkeborg. After just a few minutes, right-back Jens Martin Gammelby unleashed a fierce shot towards the Polish goal, but his shot was parried.
Silkeborg was also unfortunate not to take the lead in a promising opening to the match when a close-range finish by Collin McCowatt was denied by the woodwork after a finely orchestrated Danish attack.
A few minutes later the visitors grabbed the lead when Bernardo Vital steered home a close range volley after a corner from Jagiellonia's Danish winger Louka Prip.
Silkeborg didn't give up and often produced promising build-ups thanks to Jens Martin Gammelby and Leonel Montano on the respective wings but as the half progressed it became clear that Silkeborg lack sharpness in front of goal with Tonni Adamsen and Younes Bakiz failing to take advantage of half chances on a number of occasions.
Midway through the second half, it seemed as if Polish sloppiness, rather than Silkeborg magic, was needed for the home side to equalize.
Substitute Rami Al Hajj had a couple of brave attempts, but Silkeborg was nowhere near equalizing.
Instead, Jagiellonia defender Yuki Kobayashi could have closed the game shortly before the end, but failed to make great contact with the ball with the goal at his mercy.
The overall winner after the second leg will face the overall winner of the match between Croatian outfit Hajduk Split and Dinamo City from Albania in the playoff round of the qualification.