Venables, who will take over at Crystal Palace next season, had to field an inexperienced line-up against the World Cup finalists. The result was the biggest win in Croatia's eight-year international history.
Davor Suker, relatively fresh after spending much of the season on Real Madrid's bench, hit a hat-trick. His first goal arrived from the penalty spot in the 14th minute, after Australia's goalkeeper Zeljko Kalac had earned a yellow card for a foul on Mario Stanic.
Suker scored again in the 37th minute from a pass by Robert Jarni and, only three minutes later, Robert Prosinecki made it 3-0 with a fine individual goal.
The Croatian captain, Zvonimir Boban, found the net in the 47th minute with a superb volley and then, in the 63rd, Suker scored his third goal of the game - another penalty after he had been brought down - and was promptly substituted. His replacement, Ardian Kozniku, wasted no time in scoring No 6 in the 72nd minute. Boban finished the rout with his second goal in the closing minutes.
The victory was needed by Croatia, who had lost 2-0 at home to Slovakia last week. For Venables, though, there was no consolation.
Like Tunisia, Romania, who also face England in the first round of the World Cup, enjoyed a big win yesterday. They beat their neighbours, Moldova, 5-1 in Ploiesti.
Four players with Premiership experience were on target. Gheorghe Popescu opened the scoring from the penalty spot in the 32nd minute and another former Tottenham man, Ilie Dumitrescu, struck the third in the 49th minute after Chelsea's Dan Petrescu had scored the second in the 34th. Viorel Moldovan of Coventry and Radu Niculescu added late goals before Moldova's consolation effort from Yuri Tabanov.
South Africa concluded their World Cup preparations with a drab 1-1 draw against Iceland in a warm-up international in Baiersbronn, Germany.
The South Africans laboured through the match as their coach, Philippe Troussier, fielded an experimental line-up. They had just two shots on goal in the first half, one of them, from the Ajax striker, Benedict McCarthy, crashing into the net in the 37th minute.
However, South Africa's defence was caught pushing too far forward in the second half as Iceland broke the offside trap, and Stefan Thordason scored on the rebound for the equaliser in the 73rd minute.
A Jamaican linesman due to have officiated in the World Cup match between Japan and Croatia has been replaced because Jamaica are in the same group.
Fifa yesterday agreed to a Japanese request to withdraw Owen Powell. A South African linesman, Ahmed Salie, will run the line instead of Powell at the Japan v Croatia match in Group H.Reuse content