Romanian champion Cluj was the first team to benefit from the abolishment of the away-goals rule in UEFA competitions.
Cluj on Tuesday advanced to the Champions League second qualifying round with an extra-time goal in a 2-1 loss at Borac Banja Luka that sealed a 4-3 win on aggregate.
Under the old system scrapped by UEFA last month, the champion of Bosnia-Herzegovina would have gone through with the aggregate scored tied at 3-3 because of the goal it scored in the first leg in Romania.
Instead, the game went to extra time and Cluj scored the decisive goal in the 118th minute.
The away-goals rule was introduced in 1965 to reward teams for scoring at their opponent's stadium when international trips were typically more tiring, intimidating and tactically challenging.
UEFA believed the rule became outdated and inhibited home teams from attacking for fear of conceding a goal.
Cluj will next play Lincoln Red Imps of Gibraltar which beat Fola Esch of Luxembourg 5-0 to seal a 7-2 aggregate win.
Ferencvaros, which played in the group stage last season against Barcelona and Juventus, also advanced from the first qualifying round. A 3-1 win in Kosovo against Prishtina made it 6-1 on aggregate.
Ferencvaros will meet Zalgiris of Lithuania in the second qualifying round which is played over the next two midweeks.
Other national champions advancing Tuesday included Malmo, the 1979 European Cup beaten finalist, and Slovan Bratislava.
Shakhtyor was hosting Ludogorets in neutral Belgrade, Serbia, because of a UEFA block on playing its competition's games in Belarus amid European Union sanctions including restrictions on travel.