(CNN) -- Four-time European champions Ajax scraped into Friday's Champions League draw after edging their third qualifying round tie on away goals.
The Dutch team, who had to start in the opening preliminary stage of Europe's premier club competition after finishing second in the Eredivisie last season, drew 3-3 against Greek side PAOK Salonika on Wednesday night.
Having been held 1-1 in the first leg in Amsterdam last week, Martin Jol's team went behind when Adelino Vieirinha scored in the 16th minute.
Uruguay's World Cup star Luis Suarez leveled soon after halftime and the Ajax captain helped Siem de Jong put Ajax ahead from close range on 50 before Rasmus Lindgren made it 3-1 five minutes later.
Dimitris Salpingidis pulled a goal back immediately, and Suarez hit the post, then Ajax's Netherlands goalkeeper Maarten Stekelenburg saved a late penalty from Vladimir Ivic, whose injury-time consolation goal came too late.
In other results, Russian league leaders Zenit St. Petersburg knocked out last year's group stage qualifiers Unirea Urziceni of Romania, with Portugal international Danny scoring the only goal of the two ties 12 minutes before halftime.
Scottish side Celtic, the 1967 European champions, failed to reach the group stage for the second time in two years despite beating Braga 2-1 at home, losing 4-2 on aggregate to the Portuguese league runners-up.
Paulo Cesar added to debutants Braga's first-leg lead in the opening half, and goals to new signings Gary Hooper and Efrain Juarez were not enough to save Celtic.
Swiss side Young Boys stunned Turkish league runners-up Fenerbahce, who had a player sent off in both legs before falling to a 3-2 aggregate defeat.
Henri Bienvenu scored the only goal of Wednesday's match in Istanbul five minutes before halftime, then Miroslav Stoch was red-carded eight minutes after the restart.
Hungarian side Debrecen also played in the first round proper last season, but will not this time after losing 3-1 at FC Basel for a 5-1 aggregate defeat by the Swiss champions.
Sparta Prague made it through despite having two players sent off against Lech Poznan, with the Czech side winning 1-0 in Poland as Jiri Kladrubsky's 50th-minute penalty sealed a 2-0 overall victory.
Sparta had Marek Matejovsky and Libor Sionko sent off in the final 10 minutes, while the hosts had captain Bartosz Bosacki ordered off.
Danish champions Copenhagen won 3-2 against BATE Borisov to eliminate the only Belarusian team to have qualified for the group stage, back in 2008-09.
After a goalless first leg in Belarus, the Danes led through Cesar Santin and William Kvist before Artyom Kontsevoi and Pavel Nekhaychik leveled and Vitali Rodionov hit the bar, but Dame N'Doye netted the winner.
Serbia's Partizan Belgrade won 2-1 at Finnish side HJK Helsinki for a 5-1 aggregate victory, while Ukrainian runners-up Dinamo Kiev cruised into the next round with a 6-1 overall win against Belgian club Gent.
Norwegian champions Rosenborg beat AIK Stockholm 3-0 for a 4-0 aggregate win over the Swedish league winners.
While the third-round winners go into the hat for the chance to qualify for the lucrative group stage of the competition, won last May by Italy's Inter Milan, the losers will go into the draw for the playoffs of the second-tier Europa League.