Scorer: FC Basel - Streller (52)
The Swiss had beaten Manchester United, Chelsea and Tottenham in the last four years and added the five-time Champions League winners to that list to move ahead of their opponents in Group B after Marco Streller converted a 53rd-minute corner.
Liverpool have plenty of time to remedy the situation, but will hope the injured Daniel Sturridge regains full fitness for the back-to-back meetings with Real Madrid which come up next.
Basel attacked with pace and controlled possession and no shortage of aggression.
The only black mark for the hosts came in the first half when referee Jonas Eriksson halted play to retrieve a missile thrown from their hardcore fans behind one of the goals.
Liverpool never really threatened Tomas Vaclik in the Basle goal. Mario Balotelli became increasingly isolated up front and still does not offer enough in the way of workrate and movement for manager Brendan Rodgers who, on more than one occasion, registered his displeasure that the Italian was not working harder for his team-mates.
The better of the chances fell to Basel, who looked to expose the space behind Liverpool’s advancing full-backs – particularly the left-sided Jose Enrique who allowed Derlis Gonzalez, an early substitute for the injured Behrang Safari, to get the wrong side of him only for his poor first touch to run off the end of the pitch.
Simon Mignolet dealt comfortable with Basel’s first shot by Mohamed Elneny and then blocked Geoffro Serey Dey’s effort after he side-stepped Enrique and Dejan Lovren far too easily, but he was relieved to see Ahmed Hamoudi’s fierce angled attempt flash past his far post.
Lovren was only slightly more effective at the other end, missing two good chances with his head from Philippe Coutinho set-pieces.
Sterling also failed to trouble goalkeeper Vaclik sufficiently after Jordan Henderson’s raking crossfield ball dropped to him just before half-time.
Mignolet came to his side’s rescue, saving low from Hamoudi, but Lovren’s panicked concession of a corner proved costly as Liverpool were exposed yet again at a set-piece as the goalkeeper clawed out the flick-on from Taulant Xhaka’s corner but could not prevent Streller smashing home from close range.
Liverpool’s response was a viciously dipping 35-yard Balotelli free kick which Vaclik parried into the path of Lazar Markovic whose follow-up was blocked, although the 20-year-old Serbian was far more culpable in missing the target from Enrique’s low cross with 14 minutes to go.
Even Steven Gerrard, so often the saviour in such situations, could not rescue a point with a late free kick straight at Vaclik.