Paris: Celtic won 2-0 in Tallinn on Tuesday night to complete a 7-0 aggregate Champions League qualifying victory over Estonian champions Nomme Kalju.
Another former champion, PSV Eindhoven, went out, eliminated on away goals by Basel.
A first-half own goal and a powerful strike by Marian Shved ensured the Scottish champions, who rested several regulars, a comfortable passage through the second qualifying round.
Celtic, a former winner of the competition, will meet Cluj in the third round of qualifying.
The Romanians drew 2-2 at Maccabi Tel Aviv and advanced 3-2 on aggregate.
With his club five goals ahead and kicking off their Scottish Premiership defence on Saturday against St Johnstone, manager Neil Lennon made six changes from the first leg.
Christopher Jullien, the £7 million signing from Toulouse, made an untroubled debut at the back and goalkeeper Craig Gordon kept a clean sheet in his first appearance since December.
Olivier Ntcham started for the first time since upsetting Lennon by suggesting he wanted to leave Celtic.
“I’m very happy with the scoreline, with the performance, and very happy with the scoreline over the two legs,” Lennon said. “I’m happy to get important minutes into some of the players who haven’t had that luxury, and to come through injury free.”
Celtic took the lead when Kalju’s Aleksandr Kulinits sliced the ball into his own goal.
In second half added time, Shved fired into the top corner of the goal from outside the area.
The game was played in the 14,500 capacity national arena rather than Nomme Kalju’s Hiiu Stadium which holds 650.
Celtic have two more rounds to negotiate to reach the group stages, starting against Cluj next week.
PSV travelled to Switzerland holding a 3-2 lead and lost 2-1 to go out on away goals.
Defender Eray Comert gave the home team the lead after eight minutes with a powerful long-range drive that went in off the underside of the bar.
Portuguese striker Bruma replied after 23 minutes with a powerful header on the run from just inside the box.
PSV outshot the home team 16-8, but lost to a goal by a Dutchman playing for Basel.
Much-travelled striker Ricky van Wolfswinkel made up for a couple of glaring misses by scoring the winner in the 68th minute.
In the next round, Basel will travel across the Alps to face Austrian club LASK from Linz, who had a bye to the third qualifying round.