After a goalless first half, Irvine once again gave Australia the lead, having scored the opening goal in their 2-0 win over India in their first group game.
The victory moved 2015 champions Australia to six points while Syria have one point from two games.
"I was very happy with our defensive performance. That's two clean sheets that we've started off with now in the Asian Cup. Overall, I know we will improve as we go on," Australia coach Graham Arnold told reporters.
"One of the things we've been working on is Jackson, he gets into the box well and he has goalscoring ability ... Jackson has now scored two goals in two games and he's getting in those positions to score, which is important."
Roared on by their supporters, Syria had started on the front foot and the Middle Eastern side nearly opened the scoring through Pablo Sabbag, who hit the post in the fifth minute.
But Australia quickly settled down and soon controlled possession, with most of the action in Syria's half while goalkeeper Mathew Ryan cut a lonely figure at the other end.
Arnold had hoped to see improvement in their set pieces and they had the opportunity to score from a corner when Gethin Jones headed the ball to the far post, but Irvine was unable to get on the end of it.
SYRIANS SILENCED
However, Irvine made no mistake in the 59th minute when he collected the ball on the turn inside the box and poked it past keeper Ahmad Madanieh to silence the Syrians who made up the majority of the 10,097 fans inside the Jassim Bin Hamad Stadium.
"You've got to find that little moment that can win you a game and fortunately it fell to me again today," Irvine said after his second straight player of the match award.
Australia had a scare minutes after taking the lead when Mouaiad Al-Ajaan unleashed a strike from long range and Ryan nearly bundled the ball into his own net, but he quickly recovered to grab it before it crept over the line.
Syria tried their luck from distance several times but Australia held firm to keep a second clean sheet.
Syria coach Hector Cuper took solace in his side conceding only one goal so far in the tournament after a 0-0 draw with Uzbekistan in their group opener.
"We have good attacking players but they lacked the last touch. They were unlucky, they hit the post today," he said.
"We'd have been more worried if we couldn't reach their box, but Australia have a great defence and the performance of my players gives me assurances for the next game."
Syria face India in their final group match on Tuesday while Australia play Uzbekistan, who extended their unbeaten record over India to seven games with a comfortable victory -- their fifth in a row against the south Asian side.
Goals from Abbosbek Fayzullaev and Igor Sergeyev gave Uzbekistan a 2-0 lead inside 18 minutes as they capitalised on India's sloppy defending.
Sherzod Nasrullaev added a third in first-half added time when he tapped in from his own rebound off the post to put the game out of reach
