Clear chances were rare in the first period for both sides as Celtic took their time settling into the match.
The hosts did have the best opportunity shortly before the break but Demba Savage failed to test Fraser Forster with his shot.
Celtic still looked short of their best as they returned for the second half and were nearly punished by Helsinki when Mathias Lindstrom's header just went wide of the post.
The Scottish champions did find a crucial goal in the 66th minute when Charlie Mulgrew found space to deliver an accurate cross towards Jo Ledley, who made no mistake from close range.
However, Neil Lennon's side were unable to relax in the final stages of the game after Victor Wanyama was given a second yellow card for a late tackle on Mika Vayrynen.
Any hopes of a dramatic fightback from Helsinki were dashed five minutes from time as Ledley started a Celtic counter-attack before finding Georgios Samaras and the Greek striker finished powerfully past Ville Wallen.