SO much for being susceptible to the jitters.

So much for maybe falling on their faces when they had one foot over the threshold of the Champions League proper. Celtic are still an inexperienced team in Europe but last night they were as nerveless as a bold lad making his first trip to the dentist.

Helsingborgs were modest opposition but Celtic were the masters of them and also of their own temperament. They were composed in not only defending their Champions League play-off lead from the first leg, but doubling it.

Gary Hooper's opening goal perhaps ought to have been disallowed for offside. Helsingborgs were furious about it – it changed the feel of the second leg – but in truth Celtic were comfortably superior over the two matches. Once the goal was in, the Swedes required three on the night to survive and there was no prospect of that. Victor Wanyama wrapped things up with a late header.

By then, thousands of Celtic supporters looked upon the Swedish champions but barely gave them a thought. Instead, they indulged themselves by imagining who would be at Parkhead in their place. Would it be Barcelona, Real Madrid or maybe Chelsea from pot one in today's draw? Juventus, Manchester City or Valencia from pot two?

All that and the best part of £20m flowing in, too. One or two of the men who secured this bounty will find their places under additional pressure as Celtic inevitably show that some of the wealth is burning a hole in their pockets.

They actually qualified for the group with a solid, unspectacular performance driven by Georgios Samaras, with admirable contributions from both Wanyama and Kelvin Wilson. They won – maintaining their 100% record in four qualifiers against HJK Helsinki and Helsingborgs – with something to spare.

Samaras decided he'd be unplayable for a while. The manager Neil Lennon started with him on the left but he was like a daddy-long-legs on a window pane, causing annoyance all over the place. When he ambled at Helsingborgs down the left, they couldn't cope. When he swopped with Kris Commons and played in the hole, they couldn't cope. Even when he popped up on the right, they couldn't get the ball off him there either. Some of his attacks ran out of steam in the penalty area but frankly he scared the life out of the Swedes. There was a standing ovation when he was substituted 20 minutes from time.

For all its importance, the opening goal contained two mistakes, one by Scott Brown, the other by referee Carlos Carballo and his assistants. Commons' corner reached Brown via James Forrest and the captain's shot from the edge of the box was a mess. The sclaffed shot fell to Samaras on the edge of the six-yard box. He was poise personified, immediately converting Brown's wayward effort into a cushioned low pass to Hooper. He buried a routine finish in the goalmouth although it was a mystery that none of the officials recognised the offside position from which he took possession. The referee was deaf to the animated protests of Age Hareide on the touchline. The manager gestured angrily to the footage on the giant screens but he was a man alone.

The goal killed the contest and crystallised Parkhead's mood. Tension melted away, replaced only by prolonged jubilation. Their team was home and dry. So what that they created few other threats on Par Hansson's net until the closing minutes? Samaras had earlier slalomed through two defenders before striking an angled shot gathered by the goalkeeper, and there was a penalty claim – correctly ignored by Carballo – when a Forrest dribble was ended by Joseph Baffo's tackle. Forrest later smacked a shot off a post.

Helsingborgs did what they could. They were mobile and bright enough but created fewer chances than in the first leg and never really looked capable of hurting Lennon's defence. Alejandro Bedoya, the former Rangers man, and Christoffer Andersson showed flashes of invention and some dogged tackling. A free-kick from the latter at least demanded a save from Fraser Forster early in the second half and then the striker, Nikola Djurdic, sent a fine chance into the side-netting.

All of it was little more than raging against the dying of the light. Generally their efforts were mopped up by Charlie Mulgrew and Wilson, who put in some fine tackles and interceptions. Wanyama and Brown offered another layer of protection. Brown had returned from injury, as had Samaras and Commons.

When reflecting on the match, Celtic can take satisfaction on getting the job done having sold Ki Sung-Yueng and temporarily lost Joe Ledley, Biram Kayal and Anthony Stokes to injuries. There was more than enough pleasure for them without the embellishment of a second goal, but they got one anyway when Commons' cross was rammed home by Wanyama's powerful header.

The Champions League isn't just about money and glamour – it can be brutal and unforgiving to inexperienced teams – but last night it did nothing but smile on Celtic.