Leading 1-0 from the first-leg in Iceland and starting the match in top gear, Celtic wasted little time as defender Virgil van Dijk helped himself to a brace within 20 minutes to ensure a comfortable night for the Scottish champions .
Striker Teemu Pukki grabbed a third before the break as Celtic played with impressive pace and purpose to confirm their place in the next round against either Irish outfit St Patrick's Athletic or Polish side Legia Warsaw.
The second-half was academic. Celtic had reportedly rejected a bid from Southampton for goalkeeper Fraser Forster before the match but the England international was mostly a spectator as the Hoops kept a firm grip on proceedings, with Pukki adding a fine fourth in the 71st minute to paint a proper picture of the home side's superiority.
There was a decent crowd and atmosphere inside the home of Scottish rugby - used as Celtic Park is out of commission due to its use in the Commonwealth Games in Glasgow - and they should have seen Pukki put Ronny Deila's side ahead in the fifth minute when he was cleverly set up by Kris Commons.
However, from inside the box and no challenge imminent, the Finnish striker drove straight at Stefan Magnusson, with the Reykjavik goalkeeper making a good save from Hoops striker Leigh Griffiths seconds later, the resultant corner coming to nothing.
However, the opening goal was not too long in arriving.
In the 13th minute Commons' corner from the left was headed towards goal by skipper Charlie Mulgrew and, with Magnusson flailing, the ball appeared to come off Van Dijk's knee and into the net from a couple of yards out.
The Hoops' second also came from a corner and when the ball landed at right-back Mikael Lustig at the far side of the box, he guided his header towards the back post where Magnusson was again grasping air as Van Dijk headed into an empty net.
The visiting goalkeeper redeemed himself a little in the 24th minute with fine save on the stretch from Pukki's powerful drive but three minutes later he was helpless as the Parkhead forward eventually got his name on the score sheet when he slid the ball in from two yards after being set up by Callum McGregor.
Celtic were in complete control with the limited visitors simply out of their depth.
Magnusson had to contend with a series of efforts on his goal, one in particular from Pukki in the 38th minute just fizzing past his right-hand post.
The second half looked to be about how many Celtic would score and they came close to making it four in the 50th minute but Griffiths' snap-shot from 20 yards hit the side-netting.
A game of attack versus defence was taking place with the Parkhead side pressing for more goals but slowly, and unsurprisingly, the tempo dipped.
The Celtic fans, happy with what they had been watching, chanted and serenaded their side to the final whistle, stopping to cheer Pukki when he rounded the goalkeeper at the edge of the box before slamming the ball high into the net for his second, his own celebrations cut short when he realised he was to be immediately replaced by Liam Henderson.
The substitution was booed, mostly in a good-natured fashion, by the Parkhead supporters, perhaps wishing the striker could have stayed on to get his hat-trick.
However, Commons almost provided them with another goal with eight minutes remaining, his left-footed drive from Lustig's cut-back crashing off the inside of the post before flying to safety.
- Sports & Recreation
- Teemu Pukki
- Kris Commons