The Serie A strugglers, who appointed Carmignani on Wednesday after sacking Silvio Baldini at the weekend, came from a goal down to defeat Besiktas 3-2 to progress from Group B along with Athletic Bilbao and Steaua Bucharest.
Santi Ezquerro hit a hat-trick for Bilbao who produced the performance of the night in demolishing Standard Liege 7-1 away from home to win the group.
Joining them in Friday's draw for the first knockout round were Basel, Sporting, Sochaux, Austria Vienna and Real Zaragoza who all sealed their passage on Thursday.
Parma, UEFA Cup winners in 1995 and 1999 but now struggling to cope with financial hardship, started the night bottom of the tightly-bunched group, and had to defeat Turkey's Besiktas to keep their European campaign alive.
EARLY BLOW
The home side were dealt an early blow when keeper Gianluca Berti palmed the ball invitingly into the path of midfielder Okan Buruk to fire the visitors ahead after just six minutes.
Italy international Alberto Gilardino equalized shortly after but then had a penalty easily saved by Ramazan Kursunlu.
Defender Giuseppe Cardone headed home from a corner to hand Parma a 2-1 interval lead and Daniele Degano added a third on the hour with a long-range effort. A goal two minutes from time from midfielder Tumer Metin set up a tense finale but Parma held on.
"There's still a lot of work to do, but this is a win that will boost our morale. It's always a special pleasure to do well in Europe," said Carmignani, who briefly took charge as caretaker coach in 2002.
"The work Baldini did provides a good foundation on which to build. To be successful, we need to believe in ourselves. Now we've got to start thinking about Sunday's match (against AS Roma)." Parma languish in 18th place in the 20-strong Serie A.
Athletic Bilbao, who had not won an away match all season except in the Spanish Cup, went goal crazy in the pouring rain in Liege.
The Spaniards made a flying start with Ezquerro scoring twice in the first nine minutes. In a frantic opening, Oguchi Onyewu pulled a goal back before Liege keeper Vedran Runje superbly saved Andoni Iraola's penalty.
Fran Yeste made it 3-1 at the break and in a one-sided second half further goals followed for Ezquerro, Andoni Iraola, Asier Del Horno and Joseba Etxeberria.
BASEL THROUGH
Switzerland's Basel secured the win they needed to go through thanks to a 53rd-minute header from Argentine Cesar Carignano which was enough to overcome 2002 winners Feyenoord 1-0.
The Dutch side, along with Schalke 04, had already qualified and the defeat still sent them through as Group A winners on goal difference as the top three sides finished on seven points.
Ferencvaros's 1-0 win away at Hearts lifted the Hungarians above the Scottish club into fourth place but both teams were eliminated.
Last season's semi-finalists Newcastle United finished the group stage unbeaten and sealed top spot in Group D on 10 points with a 1-1 draw at home to Sporting, good enough to also send the Portuguese side through in third place.
Craig Bellamy's looping header after a long ball had been flicked on gave the Premier League side an early advantage but Miguel Custodio equalised with a header from a free kick.
The runners-up place went to France's Sochaux, who needed a late goal from Mickael Isabey to defeat eliminated Panionios 1-0.
Real Zaragoza, who drew 1-1 away at Club Bruges and Austria Vienna, who won 2-1 away at Utrecht, sealed their passage from Group C. Dnipro Dnipropetrovsk, who were not in action, topped the group on nine points.
In Friday's draw the group winners will play a team that finished third in a different UEFA Cup group while the runners-up will meet one of the eight clubs dropping down from the Champions League.
The UEFA Cup final is at the Jose Alvalade Stadium in Lisbon on May 18.
