There Yugoslavia overcame the group stage with a win against France and a draw against Brazil thanks to a goal by Zebec.

In his club side Zebec evolved more and more to be the leading player in midfield, a position for which he was most suitable due to his intelligence.

In the second round, then the quarterfinals, the team of the era, Real Madrid, put an end to Yugoslavia's first entry into this new competition as a home 3–0 win against the Iberian glamour side was insufficient to compensate for a 0–4 defeat at the hands of Alfredo Di Stéfano and Co. in the Spanish capital.

On the domestic scene, Partizan remained in the shadow of the big two of those days, Hajduk Split, and Crvena Zvezda (Red Star Belgrade).

By the time the 1958 FIFA World Cup in Sweden took place Zebec had become the captain of the national side.

In the group stages, draws against Scotland and Paraguay and a win against France was enough to enter the quarterfinals, but, as four years before, Germany put an end to Yugoslav ambitions.

For Zebec it was then too late for the big-time clubs, so the German second division side Alemannia Aachen may not have provided a great opportunity for renewed success on the pitch, but for Zebec it was a valuable two years in which he could acquaint himself with the country in which he would celebrate his greatest successes as coach.

The aggregate result in the first round encounters with Czech side Spartak Brno was 2–2, and only the toss of a coin saw Dinamo advancing.

For Zebec there now followed a stay of almost two years with VfB Stuttgart, then a team with aspirations of joining the top of the league.

He led the unimpressive team, which was in his second season reinforced with German international Horst Köppel and the Austrian midfielder Hans "Buffy" Ettmayer to positions 12 and 8, respectively.

The 0–0 draw at home meant the end of the road for the Croatians, but reaching this semifinal remains the greatest international success for them to date.

Leeds ended up missing out on winning this tournament by the tightest of margins losing the final against AC Milan 0–1.

The team finished the national league a disappointing 9th, but the defence of the Yugoslav Cup through a victory against champions Red Star Belgrade assured a memorable season eventually.

The club, which then had a liquor manufacturer on a spending spree as main sponsor, engaged Zebec in search of better times.

Zebec hired two fellow Yugoslavs, the entertaining right winger Danilo Popivoda and midfielder Aleksandar Ristić.

Coupled with national team goalkeeper Bernd Franke and other notable players this side played refreshing quality football and often featured right on top of the table.

In his fourth and last year with the club the 1974 FIFA World Cup winner Paul Breitner joined the team coming from Real Madrid.

In his first season, he formed a competitive unit around wing back Manfred Kaltz, striker Horst Hrubesch.

As it was, the players complained about the harsh training at that late stage of the season, and critics said that it was the reason why Hamburg inside four days of the final also lost a decisive match which consigned them to runners-up in the league.

Aleksandar Ristić became his successor for half a year, before Ernst Happel took Hamburg to renewed glory.