Australia will play in Group C along with France, Peru and Denmark at the World Cup, which gets underway next week.
After qualifying for Russian Federation 2018 with Saudi Arabia but quitting due to personal terms, Van Marwijk was appointed in charge of Australia's World Cup squad.
This year's tournament will take place between June 14 and July 15 at 12 stadiums across 11 cities in Russian Federation.
Following a goalless first half at the Groupama Arena, the deadlock was finally broken in the 74th minute by 19-year-old Arzani, who had started the match on the bench but came on for Robbie Kruse in the 73rd minute.
In sight of a third-straight clean sheet, Sainsbury's headed back-pass wrong-footed substitute gloveman Brad Jones to trickle into the net for an embarrassing equaliser.
THE salaries of eight Socceroos coaches are coming directly out of the back pocket of new coach Bert van Marwijk, it has been revealed.
Camera Icon Socceroos assistant coach Mark van
"I need them because they know how I work, they know how I want to work, they know how I want to play", van Marwijk said.
"When you want to have a chance in the World Cup, those things must be very, very professional and I think that's the case now".
Van Marwijk stuck with the same starting side in Budapest as he did in a 4-0 win over Czech Republic last week.
Hungary's attacks were more opportunistic than well-orchestrated.
Jackson Irvine made the final switch to Arzani, who stepped inside two defenders onto his right foot before whipping away a low shot that took an awkward bounce before squirming under Denes Dibusz.
Van Marwijk's backroom team are all people he has worked with in the past and include four assistant coaches, two video analysts and two scouts. "We won, but I already told my players I wasn't satisfied".