With Rangers demoted to the third division, entry into Europe's elite tournament and the millions that go with it are vital as Celtic bid to make up for the loss in attendance money caused by the absence of their fiercest rivals and the home side started at a frantic pace.
However, the Hoops failed to take their early chances and conceded a costly away goal just 90 seconds after the break when Rasmus Schuller finished from close range.
Gary Hooper fired home a 54th minute equaliser after being picked out in the box by Georgios Samaras before Charlie Mulgrew headed home a 61st minute winner.
It leaves Celtic with a tough task in the return leg next week as they bid to make the group stages of the competition for the first time since 2008.
"I think Helsinki can count themselves pretty fortunate that it is only 2-1. We have got a week to get ready and the players will benefit from that game tonight," Celtic manager Neil Lennon said.
"We went a goal down and showed plenty of character and they clawed their way back into the game brilliantly and for a bit of luck or better finishing they would have won the tie more comfortably."
HJK coach Antti Muurinen said the result gave his side a good chance to go through.
"It was especially important for us to get a goal away from home," Muurinen said.
"I still believe we have a good chance to win and our team played with good spirit today."
At Celtic Park, Kris Commons recovered from an ankle knock to join Hooper up front while Irish striker Anthony Stokes had to be content with a place on the bench.
In a whirlwind start the Hoops had a chance straight from kick-off when Hooper was sent racing clear but he sent his strike into the side netting.
Barely a minute later Victor Wanyama sent a golden chance wide as he connected with a Commons corner at the back post.
Celtic were appealing for a penalty in the 14th minute when James Forrest appeared to be pushed as he went to head a Samaras cross but referee Miroslav Zelinka ignored their pleas.
Hooper was the next to have a chance but he completely miscued Forrest's cut-back and Joe Ledley volleyed wide as the ball broke to him.
The home side were completely dominating and only a good save from keeper Ville Wallen stopped a Ledley strike from the edge of the box sneaking in.
However, Helsinki slowly settled into the match and Adam Matthews got an important touch to take the ball off Demba Savage as he looked to pull the trigger in the box.
Fraser Forster then had to be at full stretch to prevent Joel Perovuo's fierce drive from bursting the net.
Celtic failed to heed the warning signs and 90 seconds after the break they found themselves behind.
Schuller broke into the Celtic box and while Forster saved his initial shot with his feet the ball broke back to him and he fired it past the helpless keeper from four yards.
The goal seemed to be the wake up call Celtic needed and they were nearly level a minute later when Commons sent a strike off the base of the post which then rebounded off the back of Wallen's head and went just wide.
The Hoops got an equaliser in the 54th minute through Hooper. Commons picked out Samaras wide on the left and his cross field pass to Hooper split the Helsinki defence and allowed the striker to fire past Wallen from close range.
Celtic committed more and more men forward and took a 61st minute lead when the unmarked Mulgrew sent a downward header into the turf which bounced over Wallen and into the roof of the net from Commons' corner.
Source: AFP
Source: AFP