The Finnish side went ahead within 90 seconds of the second half through Rasmus Schuller, however Celtic were quick to respond through Gary Hooper on 55 minutes, while Charlie Mulgrew wrapped up the win six minutes later.
The first half saw Celtic in total control and they even had a chance to take the lead in the opening minutes when Hooper found himself in a shooting position down the right wing. However, unbalanced, his shot hit the side netting.
The Scottish champions had calls for a penalty dismissed as early as the 14th minute when a Georgios Samaras cross from the left was connected with by James Forrest. His shot went wide of the right-hand post, but he appeared to be pushed in the back by his marker as he jumped. The referee was not interested.
Things may have evened themselves out shortly afterwards when HJK had their own call for a penalty. As Juho Makela made good ground in the Celtic box Victor Wanyama made a clumsy challenge from behind. However, the call from the referee was the same - no penalty.
Celtic's Scott Brown had a slightly tenuous penalty call in the 27th minute when he turned his marker in the box before going down. The crowd thought it was a penalty but the referee didn't agree.
At this stage Celtic were in total control and using both wings to their full advantage, but remained unable to break the deadlock.
HJK had a chance to open the scoring in the 35th minute when Demba Savage brought the ball inside before passing to Joel Perovuo who saw his shot turned away by Fraser Forster in the Celtic goal. The corner was attacked by HJK but the header was sent well over the bar.
Just before the half time break, Emilio Izaguirre played a sublime through ball towards Hooper who was in a perfect position to score. Unfortunately for Hooper he could only take a fresh air swing at the ball and wasn't even able to trouble Villie Wallen in the HJK goal.
After the sides emerged to begin the second half the game changed completely. HJK seemed more organised in defence and more coherent going forward. Celtic felt the full effect of this new found confidence when a run down the right by Sebastian Mannstrom saw him play the ball in to Rasmus Schuller who beat Forster at the second attempt.
This sparked Celtic into life and they responded through Hooper in the 55th minute. Samaras picked up the ball on the right wing before playing a low pass across the face of the goal which was slotted into the bottom left hand corner by Hooper.
Not satisfied with having handed an away goal to HJK, Celtic pressed on and finally took the lead in the 61st minute, Mulgrew pouncing on a deflection from the HJK keeper.
Two minutes later Celtic could have made it three as Izaguirre played a ball into Kris Commons in space. Commons's shot seemed to have the keeper beaten but flashed past the outside of the post.
This would be Commons's last action as he made way for Anthony Stokes, who try as he might, couldn't find the back of the HJK net.
As the tie rolled into the final quarter HJK began to fade and put every man behind the ball. This gave Celtic the space to play again. However, shots from Brown and Mulgrew missed the target and kept the game at 2-1.
Celtic continued to threaten from set pieces and raiding runs down the wings. However, try as they might, they couldn't add to their lead and at the final whistle the Finns may have been the happier side, taking an away goal back to Helsinki.
Celtic's Samaras and HJK's Mika Vayrynen will carry yellow cards in to what will be a very different game next Wednesday night. The second leg will take place on HJK's synthetic surface and Celtic will look to score early to avoid an early season nail-biter.