Valdan Nimani’s 39th minute strike had levelled the tie following Differdange’s 1-0 success in Albania but strikes from Omar Er Rafikb – in the 55th and 75th minutes – swung the tie back in the home side’s favour.
Henry Ndreka, Erjon Vucaj and Taulant Sefgjini were all dismissed for second bookable offences as the visitors chased the game.
FK Rudar Pljevlja join them in the second qualifying round following a 1-1 draw against MIKA Ashtarak in Armenia, which sealed a 2-1 aggregate win.
Rafayel Ghazaryan had opened the scoring for the home side on the stroke of half-time to level the tie, but Nenad Stojanovic’s 85th minute strike ensured the Montenegrins' progression.
Jeunesse Esch lost 2-1 away at TPS Turku but went through courtesy of last week’s 2-0 home success.
Chu Wang grabbed the crucial strike with 10 minutes to go to level the tie on the night following Alexandre Vitali’s 38th minute own goal.
Roope Riski struck with 87th minutes gone but the Finnish team were unable to force another that would have sent them through.
UEFA Europa League Qualification round one second leg matches
FC Differdange 03 (Luxembourg) - Laci (Albania) 2-1 (halftime: 0-1) First leg: Laci - FC Differdange 03 0-1. FC Differdange 03 win 3-1 on aggregate.
TPS Turku (Finland) - Jeunesse Esch (Luxembourg) 2-1 (halftime: 1-0) First leg: Jeunesse Esch - TPS Turku 2-0. Jeunesse Esch win 3-2 on aggregate.
MIKA Ashtarak (Armenia) - FK Rudar Pljevlja (Montenegro) 1-1 (halftime: 1-0) First leg: Rudar - MIKA Ashtarak 1-0. Rudar win 2-1 on aggregate