
Beasley scored in the 80th-minute to complete a 3-0 aggregate win although the home side had a strong claim for a penalty when Kirk Broadfoot challenged Slaven Stjepanovic in the Rangers area.
Red Star play Estonia's Levadia Tallinn Wednesday, holding a slim 1-0 advantage from the first leg.
Dinamo Zagreb, meanwhile, face Bundesliga side Werder Bremen in the next round after beating Slovenian title-holders NK Domzale 3-1 on the night and 5-2 on aggregate.
Ognjen Vukojevic opened the scoring for Dinamo on 18 minutes and Tomo Sokota doubled the lead four minutes later. Dario Zahora pulled one back for Domzale on 27 minutes but Brazilian Sammir made it 3-1 in the second half.
Copenhagen needed extra time to overcome Beitar Jerusalem after a goal from Israel striker Barak Yitzhaki on 61 minutes meant the tie finished 1-0 to Beitar and 1-1 on aggregate after 90 minutes.
However, Swedish forward Marcus Allback netted for the Danish side in the first period of extra time for a 2-1 aggregate win. Copenhagen now face Portuguese giants Benfica in the next round.
Finnish side Tampere United made it to the third qualifying round for the first time in the club's history thanks to a 1-0 away win against Levski Sofia that secured a 2-0 aggregate win.
Jari Niemi netted the only goal of the game five minutes before half-time to set up a probable tie against Norwegian side Rosenborg Trondheim, who play FK Astana at home Wednesday leading 3-1 from the first leg in Kazakhstan.
The remainder of the second qualifying round ties take place Wednesday with the third round first-leg ties on August 14-15.
DPA