Rosenborg set up Champions League tie with Celtic
Dundalk forced the tie to go into extra time after two 1-1 draws.
Celtic will face Rosenborg in the third round of Champions League qualifiers.
The Norwegian side beat Dundalk 2-1 after extra time, following two 1-1 results in either leg of their respective second round ties.
Matthias Vilhjalmsson struck the winning goal midway through the added spell after Brian Gartland's strike had been cancelled out by Yann-Erik de Lanlay in the first half.
Dundalk also took the lead in the first leg that was played in the Republic of Ireland last week with David McMillan opening the scoring before Tore Reginiussen equalised.
The first leg will be played at Celtic Park on Wednesday, July 26 with the return leg in Norway the following week.
Rosenborg missed out on the group stages of a European competition last season after losing to APOEL in the Champions League third round qualifier and then Austria Wien in the Europa League play-offs.
They last faced Celtic in Europe during the 2001-02 Champions League campaign and more recently were knocked out by St Johnstone in the Europa League three seasons ago.
Celtic beat Linfield 4-0 in the second leg of their tie, winning 6-0 on aggregate.