Basel stunned Roma at the Stadio Olimpico to get their Champions League challenge up and running.
The Swiss outfit took a 12th minute lead through Alexander Frei before Marco Borriello restored parity in the 21st minute.
Samuel Inkoom put the visitors back in front before half-time. Roma midfielder Rodrigo Taddei was unlucky not to equalise in the 58th minute with his effort rebounding off the post.
But deep in stoppage time, substitute Adilson Cabral put the game beyond Roma's reach to cap a wonderful night for the visitors.
The result, Basel's first win in the competition, saw the Swiss club climb to third place, level on three points with Cluj and Roma after three games played.
Bayern Munich beat Cluj 3-2 in the other group game tonight to maintain their 100% record.
Basel had suffered consecutive defeats before tonight's game but they were able to get off to a strong start.
They took an early lead with Frey getting Marco Streller's pass and striking the ball with his left foot from the edge of the area past Roma goalkeeper Bogdan Lobont.
It was not long before Roma had pulled level.
Francesco Totti fed Borriello inside the area and he shot past goalkeeper Francesco Costanzo.
In the 37th minute, Totti, looking for his first goal of the season, struck just wide of the far post.
Two minutes later, Frei had a goal disallowed for offside as Basel threatened and the visitors eventually went back in front.
Xherdan Shaquiri's pass found Inkoom inside the area and his diagonal effort beat Lobont.
Roma twice had the chance to equalise after the re-start but Totti and Borriello's efforts from long range went wide.
Taddei struck the post equaliser before the hour and Borriello then forced Costanzo to make a fine save from his eight-yard effort.
Benjamin Huggel should have increased his team's advantage in the 76th minute but his powerful header from Frei's cross went wide.
Roma pressed forward in search of the equaliser and they almost succeeded with five minutes remaining when Philippe Mexes latched onto Totti's cross only for his effort to go over the bar.
Basel had the last say with Cabral latching on to Scott Chipperfield's pass before driving the ball past Lobont.
# Ranieri disgusted with Roma
Claudio Ranieri was disgusted with his Roma side after they fell to a home defeat to Basel.
"We didn't win a tackle in the first half. I can't explain the change in attitude. The goal conceded on the stroke of half-time was a real blow, as we created so much and couldn't finish off our chances," he said.
"We have to keep working, but the approach in the first half was not the same as Genoa. Basel had plenty of possession and scored twice. We fought back in the second half and had many scoring opportunities, but at the moment things just aren't going our way.
"We weren't tight and were not aggressive enough. All the good things we did against Genoa went missing tonight. It was like a different team compared to the one three days ago against Genoa. We have to understand which is the real Roma: this one or the side that won at the weekend?"
"It is a Champions League game and motivation must be at the maximum. Clearly we cannot seem to maintain a consistency in terms of determination and attitude. In the first half we barely won a single tackle or committed a foul. We were sluggish and I asked the players why that was. They can't answer it and neither can I. We have to figure out why we can give our best in some games and not in others."
Roma striker Marco Borriello believes his team deserved nothing from their 3-1 home defeat to Basel. "It has been an off day for us,'' said Borriello. "It's a pity because this game meant a lot, especially when playing in front of our fans. It's a tough loss for us. We hope that it doesn't cost us dearly with regards to progressing in the competition. But we are men and we must prove to have the force to react.''
Basel, meanwhile, were delighted to have claimed their first win of the European campaign after defeats to Cluj and Bayern Munich before Tuesday's game in the Italian capital.
"We were unlucky in our previous games,'' midfielder Benjamin Huggel said. "Tonight we played really well and with great determination. We held Roma in the second half when they tried to find the equaliser. We did very well to resist and take home three points.''