While Celtic rode their luck at times, with goalkeeper Fraser Forster bailing them out a few times after shaky defending, the Glasgow side twice hit the woodwork and will feel confident going into next week's second leg after goals by Kris Commons and Georgios Samaras.
Having beaten HJK Helsinki in Finland in the previous round, Celtic – whose home form is among the better in Europe – have now won back-to-back away matches in this season’s competition.
The Hoops started well, attacking like they were the home side and taking a second-minute lead.
It was a superb goal too, created by a fantastic run and cross from Samaras on the left, and finished by Commons, who thrashed a stunning left-foot volley into the ground and past Par Hansson.
Celtic continued to press and move with intent but, a quarter of an hour in, the hosts – who are midway through the Swedish season – clicked into gear and started to dominate.
Ardian Gashi and Christoffer Andersson were controlling the tempo of the game, with Jere Uronen constantly asking questions with the dead ball and new forward signing Nikola Durdic working superbly between the lines as Scott Brown and Beram Kayal toiled in midfield.
Celtic’s midfield problems were unsurprising as Brown and Kayal had only just returned from injury – Victor Wanyama was suspended and Ki Sung-yeung omitted as he seeks set to join Premier League Swansea.
But Celtic did themselves no favours in defence, right-back Adam Matthews in particular struggling with a succession of errors from that should have been punished by the hosts.
The Welshman's slip allowed Thomas Sorum to latch on to his former Haugesund strike-partner Durdic’s clever through-ball, but Forster extended his 6’7” frame to its full capacity to bat out his finish.
Matthews was at fault again when he fell at the crucial point of a counter-attack following a Celtic corner: however he atoned for his own error with a superb recovery challenge on May Mahlangu, who dithered when played one-on-one with Forster.
The hosts were dominating possession, Celtic barely able to get a touch on the counter attack and resorting to time-wasting measures that saw Forster booked and Commons warned by Portuguese referee Olegario Benquerenca.
But, for all their territorial advantage, Age Hareide’s side were less than clinical in attack, with the final quarter-hour marked by just one half-chance as Durdic flashed a drive high and wide after a Kayal error.
Lennon made a bold tactical change at the break, replacing Kayal with young winger James Forrest as he sought to introduce some pace to his side.
It worked as, aside from a few interesting moves from the hosts, Celtic became the controlling force in the second period.
Long-range efforts from Mahlangu and Andersson barely tested Forster, whose work in the second half was mostly limited to dealing with high balls from wide and set-pieces.
The tide turned further when Kelvin Wilson was introduced, tightening Celtic defensively as Matthews was less exposed on the right.
Indeed, those early half-chances aside, Celtic seemed more than comfortable and almost doubled their lead when Charlie Mulgrew nodded Forrest’s fine cross on to the bar after a smart corner routine.
Helsingborgs’ best chance fell to ex-Rangers midfielder Alejandro Bedoya, who was lively enough but epitomised his team’s lack of cutting edge when he headed straight at Forster just before the visitors got their second.
It was a timely goal for the Hoops, and a deserved one for Samaras, who had a fine all-round game and rose highest to head a Commons corner past Hansson with a quarter of an hour remaining.
That pretty much ended the match as a contest, with the Swedes over committing men forward and repeatedly hit on the break, Samaras curling a finish just wide after a solo run, while Forrest forced a good save from Hansson and Mulgrew rattled the crossbar with a right-foot drive from just inside the area.
Commons was involved in that move too, so it was with some concern that he limped off in injury time following a late tackle by Alvaro.
Celtic fans should expect the Scotland midfielder to be rested for the weekend’s SPL clash at Inverness Caledonian Thistle, with arguably the club’s biggest game since they last qualified four years ago looming next Wednesday.