Basel beat Liverpool 1-0 on Wednesday to extend its exceptional record against English clubs in the Champions League.
Veteran forward Marco Streller pounced on a loose ball in the goalmouth in the 52nd minute to earn the Swiss champion's first Group B points after a 5-1 loss at Real Madrid.
Basel is now unbeaten in seven matches against English opposition in the competition's group stage - a run started 12 years ago when it advanced ahead of Liverpool.
"It was a perfect evening," said Basel coach Paulo Sousa, hailing a "win against an historic club like Liverpool."
Liverpool's best effort was Mario Balotelli's swerving, 60th-minute free kick from 30 meters (yards) which was blocked awkwardly by goalkeeper Tomas Vaslik.
"I thought we were too soft all over the pitch," Liverpool captain Steven Gerrard said, adding his team "didn't deserve anything."
Madrid leads the group after winning 2-1 at newcomer Ludogorets Razgrad. The Bulgarian champion also lost 2-1 at Liverpool two weeks ago.
Liverpool owed that victory to a stoppage-time penalty, and the five-time champion never looked like winners in Basel.
"I thought we were second best at times tonight," Gerrard said. "I think they are an OK team, but I wouldn't say we were blown off the park or that they were fantastic."
Streller, the Basel captain, and new coach Sousa joined in a leaping embrace at the final whistle.
The 33-year-old forward also scored the decisive goal in a 2-1 win at Chelsea last season, which the Swiss club followed up with a 1-0 victory at St. Jakob-Park. Basel started its recent run of upset victories against English visitors by eliminating Manchester United with a 2-1 win in a December 2011 group-stage match.
On Wednesday, Streller was ideally placed to take advantage of the unlucky Mignolet's second excellent save within a minute.
After the Liverpool keeper dived low to his left to push away Ahmed Hamoudi's shot, the resulting corner was deflected toward goal and he could only parry the ball to Streller.
Basel goalkeeper Vaslik was more fortunate when he pushed out Balotelli's free kick, as a follow-up shot by Lazar Markovic was blocked by defender Fabian Schaer.
Gerrard had a free kick in the 85th but this time Vaslik caught the ball cleanly.
An incident in the first half could put Basel in further trouble with UEFA while it is serving two years of probation for fan disorder last season.
Referee Jonas Eriksson briefly stopped play in the 26th minute to carry what appeared to be a used firework from the pitch.
UEFA could apply sanctions when Basel next plays at home, against Ludogorets on November 4.