The Hoops had only won once away from home in Europe in their past 33 attempts but, after a nervy first half, Joe Ledley gave them a 67th-minute lead on the night when he chested a Charlie Mulgrew cross past goalkeeper Ville Wallen.
Four minutes later Celtic were reduced to ten men when Victor Wanyama, who had already been booked, was shown a second yellow card for a challenge on Mika Vayrynen.
Despite their numerical advantage, the Finnish champions couldn't find a way back into the game and with four minutes remaining Giorgos Samaras added a second after being set up by Ledley.
Neil Lennon's side will now be seeded for the play-off round, with the draw being made in Switzerland on Friday.
Celtic welcomed back captain Scott Brown from injury at the Sonera Stadium while Mulgrew came back into the starting line-up following suspension with Anthony Stokes and Beram Kayal dropping to the bench.
The Scottish title-holders enjoyed a period of prolonged possession at the start with Adam Matthews sending in a good cross for Gary Hooper, but the ball got caught between his feet and the Finns cleared the danger.
Trailing 2-1 from the first leg in Glasgow, HJK knew that getting the opening goal would put them in the driving seat on the night, and Demba Savage was the first to threaten for the home side when he cut in from the left and let fly, but his rising shot was no real danger for Fraser Forster.
Hoops captain Brown missed a golden chance in the 13th minute when he raced clear after collecting a long ball from Mulgrew but he stabbed his shot wide from 10 yards.
And Samaras then sliced an angled shot wide of Wallen's post as Celtic continued to press for an away goal.
Just after the break Forster came to the rescue for Celtic when he made a vital save from Sebastian Sorsa's first-time shot to keep his side ahead on aggregate.
HJK then threatened from a corner as Mathias Lindstrom rose above a cluster of defenders to get a header on target but Forster scooped the ball away.
However, Ledley relieved the pressure when he grabbed a vital away goal midway through the second half.
Mulgrew popped up on the right wing and delivered a great cross for the Welshman to chest past the keeper.
Things took a turn for the worse for Celtic four minutes later when Wanyama, who had already booked for clattering into the back of Sorsa, picked up a second yellow when he took a careless swipe at Vayrynen in the centre circle.
But the Finnish champions, who were unbeaten at home in over two years, failed to find a way past a stubborn Hoops defence and their fate was sealed when Ledley cut the ball back from the by-line for Samaras to curl a shot past Wallen from 10 yards and seal a rare away win for Celtic.