Jagiellonia routed Georgia's Iberia Tbilisi 4-0 at home on Thursday, while Lech thrashed Swiss side FC Thun 7-0 in Poznań, the biggest win by a Polish club in European competition.
The second legs are scheduled for August 27.
The scoreline in Białystok did not fully reflect the match, with the visitors creating chances both early and late.
Jagiellonia was fortunate to keep a clean sheet, Poland's PAP news agency reported.
Spanish forward Jesús Imaz opened the scoring from the penalty spot in the 34th minute before Swedish forward Jeremy Agbonifo doubled the lead in first-half stoppage time.
Nigerian defender Ibrahim Alhassan scored an own goal in the 62nd, and Spaniard Sergio Lozano added a fourth in the second minute of stoppage time.
Lech, who won Poland's Ekstraklasa premiere league title last season, were even more dominant against Thun, the Swiss champions who now sit ninth in the domestic top flight after three rounds.
Swedish forward Patrik Wålemark scored twice in the 10th and 25th minutes, with Iranian forward Allahyar Sayyadmanesh adding another in the 20th.
Mateusz Skrzypczak made it 4-0 in the 31st, Radosław Murawski scored just before halftime, and Finland's Daniel Håkans added a sixth in the 48th.
Robert Gumny completed the rout in the 79th.
Lech had advanced to the Europa League qualifying playoffs after dropping out of Champions League qualifying.
In the second qualifying round of the Champions League, they beat Danish club Aarhus GF 4-1 at home but were eliminated on penalties in the return leg.
Two other Polish clubs are competing in the fourth qualifying round of the Conference League.
Górnik Zabrze, another team that dropped into the Conference League after Champions League qualifying, lost 2-3 at home to AS Monaco on Thursday.
The second leg is also scheduled for August 27.
Raków Częstochowa drew 2-2 away at Hajduk Split in their first-leg match. The return leg will be played in Poland next Thursday.
(gs)
Source: IAR/PAP