Zajec began his career at Dinamo Zagreb in 1974, aged 18. During 10 years at the club, he helped them to two domestic cup wins, as well as the league title, their first title honour in 24 years. In 1979 and 1984, he was named the Yugoslav Footballer of the Year.
He then transferred to Greek club Panathinaikos, for whom he was tremendously successful, playing over 100 games. He was also one of the best players at the time.
Following retirement, he spent two years (1989–1991) as Director of Football at former club Dinamo Zagreb before returning to Panathinaikos to run their academy. Before long, he was promoted to head coach of the club. After a period he again, he returned to Zagreb, this time as head coach, before moving once more back to Panathinaikos in 2002 to become Director of Football.
In late October 1998, Zajec replaced Zlatko Kranjčar as manager at Dinamo Zagreb (then known as Croatia Zagreb), following Kranjčar's poor record in the UEFA Champions Leaguegroup stage, where the team only managed to grab a single point in three matches (drawing with Ajax at home, before losing to both Olympiacos and Porto on the road). The team's performance in the UEFA Champions League improved under Zajec, as they managed to stay undefeated in the remaining three group matches, beating Porto and Ajax and drawing with Olympiacos. Dinamo nevertheless did not manage to go through to the quarter-finals after finishing second in their group, behind Olympiacos (at the time, only the first-place finishers and the two best second-place finishers went through).
In 2004, he moved to English club Portsmouth to take up a position as executive director. He took over as temporary team manager following the resignation of Harry Redknapp in November 2004 and was confirmed as the new manager on 21 December 2004. Five months later, he reverted to his intended director's role, following the arrival of Alain Perrin. He resigned from his position at Fratton Park on 10 October 2005 due to personal reasons.
On 25 May 2010, Zajec was appointed new coach at Dinamo Zagreb, returning to the club as coach after 11 years. However, Zajec was sacked on 9 August 2010, after leading Dinamo in just 8 competitive matches, winning the 2010 Croatian Supercup, exiting the 2010–11 Champions League in the second qualifying round, and picking up four points in the first three matches in the 2010–11 Prva HNL.