Ponor was selected to move to Deva, the location of the training facility for the Romanian national gymnastics team) in 2002, after national team coaches Octavian Belu and Mariana Bitang discovered her during a holiday in Constanţa. The next year Ponor was selected for the team for the World Artistic Gymnastics Championships in Anaheim, USA, where she won silver medals with the team, on balance beam, and on floor exercise.

In 2004, Ponor began her competitive year by going one better and winning three gold medals (team, balance beam, floor exercise) at the European Championships in Amsterdam. She then followed up that performance by capturing three gold medals on the same events (team, balance beam and floor exercise) at the Olympic Games in Athens, Greece: a gold in every event she entered. Ponor scored 9.787 to win beam, the highest women's score of the entire Olympics, and 9.750 to win floor. This performance earned her a place in the record books: no female gymnast had won three gold medals in the same Olympics since Daniela Silivaş in 1988. She was also the only gymnast in that Olympic Games to use the difficult full-in dismount. Though once a reasonably common sight in the mid '90s, it had virtually disappeared after it was devalued in the Code of Points following the 2000 Olympic Games.

2005 brought several scandals. Early in the year, Ponor was shocked when the Romanian media discovered that she had a brother that her mother, Carmen, never told her about. Ponor's father had gone to Sweden after divorcing her mother when the children were very young, and he had taken the boy with him, while Catalina stayed with her mother.

In August of that year, Ponor and teammates Florica Leonida and Alexandra Eremia left training camp and went to a party at a Bucharest night club. Consequently, the Romanian Gymnastics Federation opted to dissolve the team and sent Ponor and her teammates back to their home clubs to train. Ponor returned to her home club, Farul Constanţa, to train with her first coach, Matei Stanei.

However, 2005 also brought some triumphs. At the 2005 European Championships, Ponor again won the gold on the balance beam. But the Olympic champion failed to medal on the floor, as she went out of bounds on one of her tumbling passes and finished in fourth place with a low score. Ponor was distraught at this and was seen crying afterwards.

In November 2005 at the World Artistic Gymnastics Championships in Melbourne, Ponor was one of only two Romanian female gymnasts selected by the Romanian Gymnastics Federation to compete (the other being Florica Leonida). After an uncharacteristic wobble on the balance beam, Ponor took home only a bronze medal. She did not qualify to floor finals and did not compete on vault or bars.

The Romanian gymnastics team had a new coach for 2006, Nicolae Forminte. However, Ponor stated that she did not want to train with Forminte. Ponor went to the European Championships that year and announced that she would retire after that competition, citing lingering knee problems as the reason that she could no longer continue in the sport. She left with a final gold in the balance beam, her third European title on that apparatus, a silver in the team competition and a bronze in the floor exercise.