CELTIC survived an early scare in Iceland before roaring to an emphatic victory and booking their spot in the next stage of the Champions League qualifiers.
And the Hoops will now face Qarabag, of Azerbeijan, as they battle to get into the glittering group stages.
Ronny Deila’s men were stunned in the seventh minute when some sloppy shoolboy defending allowed the Icelandic champions to take the lead.
The Hoops rearguard was sliced open far too easily to leave keeper Craig Gordon totally exposed.
Mikael Lustig, Dedryck Boyata and Nir Bitton were all too easily elimated in the move that built on the left before Karl Fincen finished with a low shot past Gordon at his right-hand post.
Lustig was caught upfield when the ball was fed to Jeppe Hansen and Boyata was sucked out of central defence to deal with the threat.
The ball inside found Fincen unguarded and he was allowed to step away from a nonchalant challenge from Bitton before slamming in a drive that left the Hoops No.1 helpless.
It was an awful goal to concede and, at a stroke in their first move up the pitch, Stjarnan had cut Celtic’s advantage from the first leg in half.
At that stage, Deila’s outfit had a lot of possession without penetration and it took until the 22nd minute before goalkeeper Gunnar Neilsen, the team’s hero in the first leg, was called upon to make a save.
Celtic worked a neat free-kick on the left and the ball was filtered across to Stefan Johansen who fired in a low, wicked drive from just outside the box.
Neilsen got down well to block the effort, but the ball ran to Boyata who rammed it into the net from a couple of yards out.
Unfortunately, the former Manchester City defender, who scored the first goal last week, was adjudged to be offside and the ‘goal’ was immediately ruled out.
Nadir Ciftci was putting himself about without much reward, but, to be fair, the service to the Turkish striker was poor.
Although Deila expressed no problems with the plastic pitch before the game, it was obvious it was lively and bobbly and didn’t help the Celtic cause.
That was obvious when even a talented operator such as Gary Mackay-Steven was having to take a couple of touches before bringing the ball under control.
Thankfully, the Hoops got a reward for all their possession play in the 33rd minute when they levelled the tie on the night and moved 3-1 ahead on aggregate.
Yet another corner was conceded and this time it proved fruitful to the SPFL champions.
Johansen swung in it at the near post, Neilsen flapped and Bitton rose unchallenged to bullet the ball into the inviting net.
Immediately, that took some of the pressure off and Celtic might have claimed a second only three minutes later.
Lustig and Mackay-Steven combined on the right to set up Stuart Armstrong, but his corkscrew effort swept just wide of Neilsen’s right-hand upright.
And just before half-time Bitton hurted in a low right-foot drive which was well held by the sprawling Stjarnan goalie.
Four minutes after the interval, Celtic took the sting out of the tie when Mulgrew scored a second with an exquisite trademark low left-foot shot which angled past the flummoxed Neilsen at his far post.
Deilia sent on Efe Ambrose and Leigh Griffiths for Lustig and Armstrong as Celtic tightened their grip on the encounter.
Griffiths almost made a sensational appearance when, within a minute, he latched onto a headed pass from Ciftci to hammer a shot just wide of target.
Then the new Bhoy from Dundee United tried his luck twice in succession, but on both occasions his finishing efforts rose over the crossbar.
Bitton had the ball in the net again in the 68th minute, but he was clearly offside after a free-kick from Johansen found him lurking in front of Neilsen.
The Hoops netted two goals in the remaining five minutes to seal the triumph. Mackay-Steven set up No.3 for Griffiths in the 88nd minute with a sweeping ball over from the left. The striker buried it with a certain amount of aplomb.
And, deep in injury time, Mackay-Steven and Mulgrew combined on the left before the ball was switched to Johansen and the Norwegian fired a low left-foot drive into the corner of the net.
So, Celtic can now look forward to the visit of Qarabag at Parkhead next Tuesday or probably Wednesday. They upset Montenegro’s Rudar Pljevlia 1-0 to book their money-spinning tie with the SPFL champions.
On tonight’s display, despite the early hiccup, Celtic can look forward to the confrontation with confidence.
Final word on the Celtic Foundation logo on the Celtic shirts tonight – a lovely touch.
TEAM: Gordon; Lustig (sub: Ambrose 52), Boyata, Van Dijk, Mulgrew; Brown, Bitton; Mackay-Steven, Johansen, Armstrong (sub: Griffiths 62); Ciftci (sub: Rogic 82).