A second half strike by Kris Commons gave Celtic a 1-0 victory over Elfsborg, while Fenerbahce needed an injury-time penalty to draw 1-1 in its first leg match at Salzburg in the third round of Champions League qualifying on Wednesday.
After a balanced first half, Celtic had more possession in the second and made the breakthrough when Commons headed home a cross from Emilio Izaguirre in the 76th minute.
"They made it difficult for us to break them down but it was not frustrating, it was understandable," Celtic coach Neil Lennon said. "We weren't at our best, but that was always going to be the case. There is still a bit of rust there."
Looking ahead to next week's second leg in Sweden, he added: "The tie is probably in the balance, but we are confident that we can go there and get a result."
Salzburg also looked to have won after Alan's 68th minute strike, only for the Turkish side to be awarded a spot-kick in the fifth minute of stoppage time — converted by fellow Brazilian, Cristian.
There were 1-1 draws too for Molde against Legia Warsaw and APOEL vs. Maribor, while Ludogorets beat Partizan 2-1.
Tuesday's matches saw victories for the bigger clubs involved in this stage of the competition with PSV Eindhoven beating Zulte Waregem 2-0, Steaua Bucharest defeating Dinamo Tbilisi by the same scoreline and 1-0 wins for Lyon against Grasshoppers and Basel against Maccabi Tel-Aviv.
The second legs will be played Aug. 6-7.