The Glasgow giants took command of this first leg play-off in large part thanks to Georgios Samaras, who played a pivotal part in both goals, and goalkeeper Fraser Forster, who kept an invaluable clean sheet.
Greece international Samaras set up the lightning fast opener when crossing into the box for Kris Commons to volley home, then rose highest to nod in a corner from the right to seal the seal 15 minutes from time.
Fraser then managed to hold Helsingborg at bay, despite intense pressure from the Swedish champions, with Celtic manager Neil Lennon describing his keeper’s performance as “excellent”.
“Fraser’s done his chances (of getting an England call-up) no harm tonight,” Lennon told ITV1.
“I said you’d have an audience tonight and to go and show them how good you are.
“I thought he was excellent tonight. We’ve been banging the drum about him for a while, but it’s not for us to say.”
Lennon conceded Celtic were fortunate to escape leaking a goal, especially in the first half.
“We had to rely on our goalkeeper. That’s what you have to do away from home,” he said.
“The second half we were a lot better; we had to change the shape of the team.
“I’m very grateful for the two goals and the clean sheet.”
Lennon’s men will now be looking to wrap up the tie in the second leg at Celtic Park on August 29.
“The job is only half done. There is a big game at Celtic Park to come. Helsingborg showed how dangerous they can be,” he added.
If everything goes according to plan Celtic will go through to the lucrative group stages of Europe’s premier club competition, where they will be joined by the nine other victors of the play-off ties.
That could well include Dynamo Kiev, 3-1 winners at Borussia Moenchengladbach, but French side Lille have plenty of work to do after a 1-0 defeat at FC Copenhagen.
In other ties, Spartak Moscow enjoyed a 2-1 home win over Turkish visitors Fenerbahce while Swiss outfit FC Basel suffered a 2-1 loss to CFR Cluj of Romania.
In Germany, Dynamo Kiev put one foot in the Champions League’s group phase despite the hosts taking the lead.
Goals by Kiev’s Taras Mikhalik, Andriy Yarmolenko and an own goal by Gladbach’s Luuk de Jong left the hosts with a mountain to climb at Kiev’s Olympic Stadium in next Wednesday’s return leg.
Gladbach dominated the opening phase and took a deserved lead when Juan Arango’s pass found Finland midfielder Alexander Ring in space deep in the penalty area and he fired home at the near post with 13 minutes gone.
Dynamo drew level against the run of play when Ukraine defender Mikhalik fired in a shot from well outside the area which deflected off Gladbach captain Filip Daems on 28 minutes.
Kiev’s second goal eight minutes later came when Ukraine midfielder Denys Garmash split the home defence with striker Yarmolenko gratefully receiving the pass.
But he still had plenty to do as he beat the Gladbach defence to fire home past Borussia goalkeeper Marc-Andre ter Stegen to give the guests the lead.
With time almost up, striker de Jong’s first goal for his new club, having joined from FC Twente, proved to be an own goal when the 21-year-old turned the ball into the Borussia net from a free-kick on 81 minutes.