Basel keeps upsetting some of European soccer's biggest powers.
Substitute Valentin Stocker scored in the 86th minute, giving the Swiss team a 1-0 win over Bayern Munich on Wednesday night in the first leg of the Champions League's second round.
Marseille also scored late for a 1-0 home win, with Andre Ayew connecting on a header in the third minute of injury time against 2010 champion Inter Milan, which has lost six of its last seven games.
"We can score two goals, no problem," Inter coach Claudio Ranieri said.
But there was problem in the other game as the unheralded Basel's dominance left Franck Ribery to be substituted and the French international refused to shake hands with the coach Jupp Heynckes when leaving the field 20 minutes from time.
In the group stage, had Basel tied Manchester United at Old Trafford, then defeated the Red Devils to eliminate the three-time champions.
"We have beaten possibly two of the best teams in the world," Basel goalkeeper Yann Sommer said.
Basel twice hit the frame of the goal before Stocker scored in the 86th minute on a shot through goalkeeper Manuel Neuer's legs. Sommer made a string of fine saves at noisy St Jakob Park.
"It's very simple - we have an unbelievable will to win and a great understanding among the team," said 36-year-old Basel coach Heiko Vogel, once a Bayern youth coach.
A four-time winner of Europe's top club competition, Bayern hosts the Champions League final on May 19.
"The alarm bells are going to be ringing," Bayern coach Jupp Heynckes said. "We're not in an ideal position for the return game. We need to start winning."
Marseille extended its unbeaten streak to 16 games and has the advantage going into the second leg of the total-goals series, which will be played March 13.
"Nothing's done yet. I'm happy and proud because the players believed in themselves until the end," Marseille coach Didier Deschamps said. "They were up against a team that has seen it all before, with players who are used to playing in quarterfinals, in semifinals, and yet they still won."
