Kajetan Szmyt scored twice as Rangers’ defensive errors left them needing a comeback in the second leg.
On Thursday, Rangers suffered a 2-1 defeat to Jagiellonia Białystok in the Europa League third-round qualifier first leg, leaving the Ibrox side facing an uphill task in next week's return match in Govan.
Despite taking an early lead via a Guilherme Montoia own goal, Rangers conceded two goals to Kajetan Szmyt within eight minutes, with defensive lapses at the Chorten Arena proving decisive.
Manager Derek McInnes made five changes following Friday's league defeat, including a hastily arranged debut for Japanese winger Daisuke Yokota, signed from German second-tier Hannover little over 24 hours prior.
The defeat extends Rangers' continental struggles; the club has now gone eight away games in UEFA contests without a win, despite a strong second-half performance that included a near-miss late finish.
Jagiellonia, who won their first Polish league title two years ago, demonstrated growing European credentials backed by a near-capacity home crowd at the Chorten Arena.