Vladimir Volkov's 93rd-minute equaliser in the first leg was enough to see the Serbian champions through on away goals after they were unable to break down the resolute Armenian defence in Belgrade.
Vojislav Stankovic and Nemanja Kojic both missed good second-half chances for the hosts to win the tie outright, but were denied by Artur Harutyunyan in the Shirak goal.
Partizan will now meet Ludogorets in the third qualifying round after the Bulgarian outfit came back from a first-leg defeat against Slovan Bratislava to win the second leg 3-0 and claim a 4-2 aggregate victory.
Ivan Stoyanov gave Ludogorets an early lead before Spaniard Dani Abalo netted twice to seal their win.
Meanwhile, Slovenian champions Maribor used home advantage perfectly to seal their path into the next round with a 2-0 victory over Birkirkara. After a goalless first leg, strikes from Goran Cvijanovic and Mitja Viler ended the Maltese side's dreams of further progression.
Legia Warsaw also took their place in the third round of qualfying after beating Welsh side TNS 1-0 on the night and 4-1 on aggregate.
Vladimir Dvalishvili was the matchwinner for the Polish side, his 53rd-minute strike securing the win and a tie against Molde to determine who will go through to the Champions League group stages.
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