Liverpool became the latest big-name English scalp to be claimed by Basel who capitalised on the Reds' well-known vulnerability at set-pieces.
The Swiss side have beaten Manchester United, Chelsea and Tottenham in the past 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.
It was not as devastating or catastrophic as their last visit to St Jakob Park 12 years ago when a 3-3 draw -- having been three down at half-time -- sent them crashing out the competition.
Captain Steven Gerrard, the only survivor from 2002, ranked his performance that night as one of his worst and there were a few of his current tea-mates who should certainly be assessing their contributions this time around.
But Liverpool still have plenty of time to remedy the situation, although they will be hoping the injured Daniel Sturridge regains and maintains full fitness for the back-to-back meetings with defending champions Real Madrid up next.
Basle, watched by Germany manager Joachim Low who lives nearby, attacked with pace and controlled possession - something which was a familiar trait of Brendan Rodgers' side 12 months ago but seems to have gone astray with the integration of a number of summer signings - and no shortage of aggression.
In fact 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 hard-core fans behind one of the goals.
Liverpool never really threatened Tomas Vaclik in the Basle goal and that was not just down to the absence of Sturridge, who has missed the last six matches with a thigh injury but could return against West Brom at the weekend.
Mario Balotelli began to look more comfortable in the spearhead role, holding up the ball well and linking play, particularly with the overlapping Javi Manquillo -- a combination which managed to pick out Raheem Sterling only for the forward to be flagged offside before his shot against the post and converted rebound had registered.
However, Balotelli he became increasingly isolated up front and still does not offer enough in the way of work-rate and movement for Rodgers and on more than one occasion the manager 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 knock off the end of the pitch.
Mignolet, who has come in for increasing criticism recently, dealt comfortable with Basle's first shot from 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.
The England winger's block on Gonzalez five minutes into the second half had home fans screaming for a penalty but Eriksson did not agree.
Mignolet came to his side's rescue moments later 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 Gerrard, so often the saviour in such situations and who scored an added time winner to get their campaign off to a winning start at Anfield against Ludogorets -- could not rescue a point with a late free kick straight at Vaclik.
The final whistle brought huge cheers -- and jeers as Balotelli turned on his heels and marched straight down the tunnel without a second glance behind him. The 24-year-old still has plenty to learn if he is to come anywhere close to become the striker Liverpool expect him to be.