Celtic, Porto and Monaco qualified for the Champions League in Tuesday's play-offs, along with Legia Warsaw and Ludogorets.
Celtic lost 2-0 at Hapoel Beer Sheva but sneaked through on a tight 5-4 aggregate, having won last week's first leg 5-2 at home.
Hapoel dominated from start to finish against jittery Celtic but made a poor start when Maharan Radi had an early penalty saved by Celtic keeper Craig Gordon.
Even so, goals from Ben Sahar and Ovidiu Hoban left the Israelis just one goal away from a miracle, but Celtic just managed to go through by playing out time.
"It was probably the longest 90 mins I've faced as a coach," Celtic coach Brendan Rodgers said.
"I thought Beer Sheva were outstanding, they had nothing to lose. But I have to congratulate my players because all the work we've been doing in pre-season is based around that mentality. Tonight was about resilience.
"It was an amazing effort from the players on the back of what they've been through before. I'm immensely proud."
Meanwhile, Hapoel's Sahar said: "This was very cruel for us.
"We did almost everything right tonight but we were still one goal short."
Meanwhile, Porto turned in the performance of the night to win 3-0 at woeful Roma - who had Daniele De Rossi and Emerson sent off - and cruised through on a 4-1 aggregate.
Felipe, who scored a clumsy own goal in the first leg, made amends by scoring an early goal for Porto in Rome, then strikes from Miguel Layun and Jesus Corona finished off the job as the Italians lost their discipline.
"This was a wonderful effort from us," Porto's veteran goalkeeper Iker Casillas said.
"To win here in Italy is never easy ... The sendings-off certainly helped us, but we still had to score the goals."
Monaco went through 3-1 against Villarreal, with a 1-0 win in Monte Carlo, on a late goal from Fabinho.
"We knew that tonight's game was going to be difficult for us, after losing the home leg," Villarreal coach Fran Escriba said.
"We fought very hard, but we just couldn't get the away goal that would have put us back in the reckoning."
Legia also qualified 3-1, against Dundalk, with a 1-1 draw at home to the Irishmen.
Robbie Benson gave Dundalk hope with an early away goal then Legia had Adam Hlousek sent off. However, the Poles killed off Dundalk's hopes of forcing extra with a goal from Michal Kucharczyk in the very last minute.
Elsewhere, Ludogorets went through on a comfortable 4-2 aggregate against Viktoria Plzen with a 2-2 draw in the Czech Republic.
The other five play-offs will conclude Wednesday, with Borussia Moenchengladbach defending a 3-1 lead against Young Boys and with Manchester City set fair for a peaceful night after winning 5-0 at Steaua Bucharest last week.