[4] Punčec started to play tennis at the Čakovec sports club and was coached by Géza Legenstein.

[1] In 1933 Punčec fell in the semifinal of the Italian International Championships to eventual winner Emanuele Sertorio in three straight sets.

[11] The next year, he returned to the tournament and was more successful in the mixed doubles, partnering Madzy Rollin Couquerque; they ceded the title match victory to Dorothy Andrus and André Martin-Legeay.

On the French Riviera, he won the Beaulieu tournament after back-to-back victories over Bunny Austin and František Cejnar.

[17] In 1939 he was a runner-up for the Pacific Southwest Championship, losing to John Bromwich in what was described as the best match of the tournament.

[21] In 1943 it was reported that Punčec was planning to change nationality and join the Hungarian tennis ranks, although the rumor was unconfirmed.

Both players were so unfocused that Dragutin Mitić made six foot faults on serve, while Punčec botched four.

In the doubles, Bernard Destremau and Pierre Pellizza were leading 7–6 in the fifth deciding set when the Yugoslavian pair turned the tide and delivered a 10–8 victory.

It was a "collision of playing styles" as Petra approached the net frequently while Punčec operated with passing shots.

The sons were also involved in tennis and Frank was featured in the singles main draw of the 1983 French Open; he was ranked 179th in the world.