Kris Commons, who grabbed a last-gasp equaliser at Ross County in the Clydesdale Bank Premier League on Saturday, volleyed the visitors into the lead with less than two minutes on the clock following a cross from Georgios Samaras.
Hoops goalkeeper Fraser Forster made a series of saves as the Swedish champions fought back but in the 75th minute Samaras put Celtic in the driving seat for next week's second leg in Glasgow when he headed in a Commons corner.
Neil Lennon's side might have rode their luck at times but they could have won by more in the end and now face the tantalising prospect of mixing with the elite clubs in Europe for the first time since the 2008/09 season.
They stormed into an early lead when Samaras picked up a pass from Joe Ledley on the left and, when his cross came into the middle, the unmarked Commons slammed it past the helpless Par Hansson from 12 yards.
Celtic's second was a sucker punch and came when Commons' corner from the right was met by Samaras at the back post and he headed past Hansson from a couple of yards to double the visitors' lead.
The goal knocked the stuffing out of Helsingborg, who should have been dead and buried three minutes later when Samaras ran through on goal but the Greece striker curled his right-footed shot wide of the far post.
Source: PA
Source: PA