The 1986 European Cup winners defeated their Norwegian opponents 3-0 on aggregate, while Legia Warsaw hammered St Patrick's Athletic away from home to progress
The Romanian side, who won the continent's premier cup competition in 1986, eased into the third qualifying round with a comfortable 3-0 aggregate win over their Norwegian opponents.
Leading 1-0 from the away leg, Steaua finished the job thanks to second-half goals from right-back Cornel Rapa and attacking midfielder Nicolae Stanciu to set up a tie with Aktobe of Kazakhstan.
Aktobe also cruised into the third round, winning 3-0 on the night to record a 4-0 aggregate success over Dinamo Tbilisi of Georgia - with Aleksey Antonov, Igor Zenkovich and Abat Aimbetov all on target for the hosts.
Arguably the most impressive performance of the night came from Legia Warsaw, who hammered St Patrick's Athletic from Republic of Ireland 5-0 to progress.
Serbian Miroslav Radovic had earned his side a 1-1 first-leg draw with a last-gasp equaliser and he was the key for the Polish club again, netting a double as the visitors secured a 6-1 aggregate win to book a clash with Scottish champions Celtic.
Forward Isaac Kiese Thelin proved the difference for Swedish side Malmo, his 19th-minute strike ensuring a 1-0 aggregate success over Ventspils in Latvia.
Malmo, European Cup runners-up in 1979, will face Sparta Prague in the next round, and they will also be joined by fellow Scandinavians HJK.
The Finnish side claimed a 2-1 win against Rabotnicki of Macedonia to ensure a meeting with APOEL.
Elsewhere, Maribor overcame Zrinjski 2-0 and will face Maccabi Tel Aviv in the third qualifying round.