With so much at stake - UEFA earlier revealed Celtic made €30m from their run to the round of 16 during last season's competition - the Hoops fielded a strong side despite holding a 3-0 advantage from the first leg in Belfast.
Kris Commons and James Forrest then both came close to adding more as the Glasgow giants dominated the first half at Parkhead.
The Belfast part-timers improved after the break but the Hoops made sure of the win when a Georgios Samaras header made it 2-0 in the 70th minute.
Neil Lennon's side will need to overcome much tougher opposition in the form of Elfsborg for a place in the play-off round of Europe's elite competition. The Swedish champions, who won their second leg match against Latvians FC Daugave 4-0 to progress 11-1 on aggregate, will visit Celtic Park on 31 July.