The Eintracht Frankfurt midfielder's deflected volley in the 84th minute decided the feverish Asian playoff on Tuesday in the Ahmad bin Ali Stadium that will host seven games in the World Cup finals in November.
More than 4,000 UAE fans made up the majority of the crowd in the 40,000 capacity arena in the Doha suburbs, where the players were blasted with air conditioning to keep the evening temperatures down.
Australia will take on a dangerous Peru side in the same stadium in a do-or-die clash on June 13 in their quest to qualify for the finals and Arnold said he expected more from his players.
"We need to improve more. I expect another big improvement after this game," he said.
"Obviously one game at a time and I thought the UAE put in a very good performance, a tight game, but we have had good preparation ... there was more cohesion with our play and after that game I expect we will be even better against Peru.
"My focus has been on our defence because we have been sloppy, conceding goals in the last couple of (FIFA) windows. We could have scored more, but at the same time there are things that we need to tidy up as well defensively to make it tougher."
Nineteen-year-old forward Harib Al-Maazmi, who scored the winner in UAE's surprising 1-0 win over South Korea that got them to the playoff, was a constant nuisance in the first half.
- Fighting spirit -
He threatened after 18 minutes with a dangerous left wing run and again 10 minutes before the break with Socceroos goalkeeper Mathew Ryan making a top-rate block.
Minutes into the second half, Al-Maazmi again forced Ryan into a low save before attacking midfielder Jackson Irvine put Australia ahead.
Martin Boyle stole the ball on the right wing, took it into the box and Irvine, who plays for German second-division side St Pauli, tapped in at the near post.
Australia barely had time to savour the goal when Al-Maazmi again found space. His cross broke to Caio Canedo, a Brazilian who first got an East Timor passport and then qualified for the UAE in 2020, who blasted home from close range.
The game seemed destined for extra-time when Hrustic, fresh off winning the Europa League with his German club, met the ball from a corner that was only half cleared and his left-footed volley took a big deflection to find the net.
"We conceded a goal and we shouldn't have," said Hrustic.
"But we kept going, kept fighting and we took our chance, and the goal for Australia was for all the boys, for the staff, because we have been through a lot and it hasn't been easy."
UAE had been looking to qualify for the World Cup for only the second time since their debut in 1990. Their Argentine coach, Rodolfo Arruabarrena, said the UAE players "lacked the stamina in the last 15 minutes".
New Zealand take on Costa Rica in Doha on June 14 to decide the final qualifier for the tournament that starts November 21.