Callum McGregor scored on his debut against KR in manager Ronny Deila's competitive bow, while the Czech side are storming into the third qualifying round after thrashing Levadia
In Ronny Deila's first competitive match in charge of the Scottish champions, he saw his side frustrated for large spells by their Icelandic opponents in Reykjavik.
However, McGregor's well-taken goal ensures that Celtic will take an advantage into the second leg of their second qualifying round tie next week.
The 21-year-old Scot cut inside his marker and slipped the ball past Stefan Magnusson to edge his side in front six minutes from time.
Czech champions Sparta Prague are all but into the third qualifying round after hitting seven past Levadia of Estonia without reply.
Captain David Lafata was in fine form, scoring five times, while Tomas Prikryl was also on target and Toni Tipuric turned the ball into his own net in a miserable outing for the visitors.
Danko Lazovic's brace helped Partizan to a 3-0 win over HB Torshavn, while Dinamo Zagreb will hope to build on their 2-0 first-leg advantage on their return trip to Zalgiris.
Belarusian champions BATE Borisov were unable to break down a stubborn Skenderbeu side on home soil and will be keen to improve in the return encounter in Albania.
Zrinjski's visit of Maribor and HJK's trip to Rabotnicki also ended goalless, as did Cliftonville's first-leg meeting with Debrecen.
Qarabag will take a one-goal lead back to Azerbaijan for the second leg of their clash with Valletta after picking up a 1-0 win in Malta.
Chumbinho scored the only goal in a game that saw Ryan Camilleri sent off for the hosts, while Slovan Bratislava had Erik Cikos to thank for their 1-0 victory over The New Saints in the Slovak capital.
Two goals in the last 19 minutes ensured it is advantage Sheriff against Sutjeska, with Rade Prica handing Maccabi Tel Aviv a 1-0 win over Andorran outfit Santa Coloma.