Celtic battled to a 2-1 second-leg win on a frustrating night against FK Sarajevo at Parkhead.
The win sets up a second qualifying round tie against Nomme Kalju of Estonia.
Story of the game
The hosts started strongly, buoyed by their 3-1 victory in Bosnia last week, with Callum McGregor letting fly from the edge of the box twice during the opening exchanges.
His first effort fizzed narrowly wide of the post before he stung the palms of Vladan Kovacevic moments later.
The reigning Scottish treble winners opened the scoring 26 minutes in as a twisting run from Odsonne Edouard set up Ryan Christie, who found the roof of the net from inside the area.
Edouard forced Kovacevic into action once more moments before the interval as the former PSG forward saw his effort pushed safely away from goal.
The intensity of the game petered out at the start of the second half as the Hoops appeared comfortable in their 4-1 aggregate lead.
However, whenever Celtic came forward, the creative spark was from McGregor, whose driving runs caused problems for the Sarajevo back-line on what could have proved to be a frustrating evening for Celtic.
The visitors were level shortly after the hour mark as lax defending from the Celtic defence allowed Benjamin Tatar to latch onto a flick on and slot the ball underneath Scott Bain.
The impressive McGregor restored Celtic's lead on the night - and their three-goal aggregate advantage - with 15 minutes remaining. The Scottish winger drilled past Kovacevic from 20 yards out.
This goal proved the final nail in the coffin for Husref Musemic's men as the remaining quarter of an hour went by without incident.
Takeaways from the match
Hoops still lack cutting edge
Despite having now played four pre-season friendlies, Celtic lacked the intensity and endeavour to really hurt FK Sarajevo. The Bhoys created minimal clear-cut chances inside the 18-yard box and were limited to efforts from distance on the whole. Frontman Edouard look most dangerous when dropping deep to collect the ball before bringing others into play instead of getting himself into goal-scoring opportunities.
With two and a half months still remaining in the summer transfer window, Neil Lennon may still look to recruit another striker to spearhead his attack. Although Middlesbrough's Britt Assombalonga is the only striker currently linked with the club.
Bolingoli impresses on home debut
New signing Boli Bolingoli performed well in his first appearance at Celtic Park since his arrival from Rapid Vienna. The Belgian left-back showed himself to be adept at going forward and supporting the attack on a night where Celtic spent most of the time on the offensive.
However, Bolingoli admits himself that the defensive side of his game needs some work. "In my youth I was an offensive player and I am still learning my defensive parts. I know that I still need to progress in my defensive part but I have to do better. I'm a left-back so the first thing is defending" he told Football Scotland post-match.
Sterner tests lie ahead
Although FK Sarajevo provided a viable threat to Celtic across the two legs, Lennon's side were expected to progress as they did. The same is expected once again as they face Estonian champions Nomme Kalju in the next phase of Champions League qualifying.
However, there still lies considerable threats ahead before Celtic can reach the group stage and Lennon will know that his side must improve their performances if they are to go one better than last season, with the likes of PAOK and Red Star Belgrade potentially waiting in the third qualifying round.
MOTOM: Callum McGregor
The 26-year-old produced a talismanic performance on Tuesday night, combining swashbuckling runs, defence-splitting passes and long-range strikes as he proved a constant thorn in the opposition's side.
His 76th minute strike capped a fine performance from the former Notts County loanee after he had seen two previous efforts flash wide and be palmed away respectively.
Overall, manager Lennon will be pleased that his side have overcome the first hurdle on route to the Champions League group stage without major issue as at this stage it remains result first, performance second. This fixture will ultimately also go a long way to sculpting how he chooses to set up his side for the long season ahead as the Hoops once more look to juggle a domestic title defence with a successful European campaign.