Lyon became champions of Europe for the fourth time – matching the record set by Frankfurt – after beating PSG in sudden death of a penalty shootout to successfully defend their women’s Champions League title.

With the score goalless after 120 minutes and the scores level at 6-6 in the shootout, the goalkeepers each took a penalty: PSG’s Katarzyna Kiedrzynek dragged her effort horribly wide before Sarah Bouhaddi sidefooted the decisive spot-kick past Kiedrzynek into the corner and was mobbed by her Lyon team-mates in celebration.

Lyon came into the match as strong favourites, in search of an unprecedented second successive treble, having won the French League, French Cup and the Champions League last season. This year, their dominance has continued: another league title, another French Cup, 103 goals scored, six conceded and just one defeat, tellingly a 1-0 league defeat to PSG.

More than 20,000 supporters created a boisterous atmosphere, many travelling to the Cardiff City stadium from France, with the Welsh capital also set to host the men’s final between Real Madrid and Juventus at the Millennium Stadium on Saturday.

PSG were tight and compact in midfield and combative in the tackle in the opening exchanges, with Lyon’s USA international Alex Morgan – signed on loan from Orlando Pride in January – was forced off after taking a knock on her ankle. The World Cup winner had been struggling with injury prior to the match and was replaced by Élodie Thomis after 20 minutes.

Lyon nearly took the lead when Grace Geyoro almost turned a low Eugénie Le Sommer cross into her own net but the teenage PSG defender recovered well to make a crucial block three yards out.

Match winning goalkeeper Sarah Bouhaddi lifts the trophy as she and her team-mates celebrate Lyon’s fourth European victory. Photograph: Stu Forster/Getty Images

Lyon continued to dominate possession, with PSG reduced to long-range shots from Marie-Laure Delie and Cristiane, but it was the Parisian side that had the best chance of the half: Shirley CruzTraña, formerly of Lyon, latching on to a fine flick from Delie before turning inside and forcing a magnificent save from Bouhaddi. PSG finished the first half the stronger, Cristiane blazing over from 10 yards out after excellent work from Cruz Traña and Ashley Lawrence down the left.

Both sides were guilty of missing golden chances in the second period: Lyon’s Ada Hegerberg somehow stabbed wide from five yards out after Kiedrzynek had saved her initial effort, then Delie passed the ball inches wide after being put clean through by Cruz Traña. After sustaining a nasty blow to the head, Kiedrzynek was lucky that a poor punch did not fall to a Lyon player with the goal gaping.

PSG lost their cutting edge when Cruz was forced off – only the 39-year-old Brazilian Formiga, a veteran of the 1995 World Cup, showing any incisiveness – and as the game moved into extra time, both sides tired. With the normally prolific Hegerberg withdrawn for Pauline Bremer, Lyon were unable to find a way through in 120 minutes. Although PSG briefly went ahead in the shootout, it was Lyon’s nerve that held, with Kiedrzynek left absolutely distraught at the end. PSG’s defeat hit especially hard as it means they will not participate in next season’s Champions League after a disappointing third-placed finish in France’s Division 1 Fémininey. For Lyon, few would bet against them adding a fifth European title next season.