Australia are favoured to win next Saturday's return leg at the Melbourne Cricket Ground to snatch the 32nd and final vacant berth at next year's World Cup finals.
Venables and his players left Tehran almost immediately after the finish of Saturday's match at the Azadi Stadium, chartering a plane to Dubai so they could catch the first available flight back to Australia.
The former England manager told reporters before leaving the Middle East that he was pleased with Australia's performance against the Iranians, describing it as a courageous effort.
"This was always going to be rough," Venables said. "The most experienced players would have found a game like this difficult to deal with. It's important that you stand your ground. If you lose your courage, you could fold, and they didn't."
Venables said he was particularly pleased with the teenage striker Harry Kewell and the goalkeeper Mark Bosnich. Kewell, who plays for Leeds United, belied his inexperience at international level by calmly slotting home a left-foot shot to give Australia the lead in the 19th minute.
Iran equalised four minutes before half-time when the Cologne striker Khodadad Azizi slid the ball past Bosnich from close range, but the Aston Villa keeper made a series of stunning saves to secure the draw.
"We got a result, and we got a goal. We've got to be satisfied with that," Venables said.
Kewell's early strike means Australia need only a scoreless draw in the return leg in Melbourne next Saturday to qualify for the World Cup for only the second time since the tournament's inception in 1930.
Running on to a header from his strike partner Mark Viduka, Kewell controlled the ball with one touch before hitting a left-foot volley into the bottom right-hand corner.
Although the match between the Oceania champions and the fourth-placed Asian team was a pulsating affair, the players struggled to perform on a sandy and bumpy pitch that made control difficult.
Azizi coped best with the conditions and constantly tormented Australia's defence, marshalled by their captain, the Adelaide City defender Alex Tobin. "If we had been offered a 1-1 draw before the game, we'd have gladly taken it," Tobin said.
When the midfielder Naim Saadavi beat Australia's defence on the right touchline before crossing the ball, Azizi was the sharpest to react to deflect the ball inside Bosnich's right-hand post and send the 110,000 capacity crowd into raptures.
Iran's most influential player, Karim Bagheri, missed Saturday's first leg because of suspension but will be available for the return fixture in Melbourne.
Iran's new coach, Valdir Viera, believes Bagheri's return will lift his team to victory. "The players say he is 40 per cent of the team," Vierra said. "We'll score at least one goal in Melbourne."
Like Australia, Iran are attempting to qualify for the finals for the second time. On each occasion it has been at the other's expense. In 1974 Australia qualified after losing 2-0 in Iran but winning 3-0 at home. Four years later they lost 1-0 home and away as Iran qualified.
Iran: Abedzadeh; Mahdavikia, Khakpour, Payravani, Mansourian (Tahami, 64), Estili, Daei, Azizi, Shahroodi, Pashazadeh (Madjiji, 74), Saadavi.
Australia: Bosnich; Moore, Horvat, Tobin, T Vidmar, Slater (Lazaridis, 56), Foster, Zelic, A Vidmar (Tapai, 56); Kewell (Arnold, 86), Viduka.
Referee: P Pairetto (Italy).Reuse content