The Socceroos had lost their previous five games and were faced with setting a new record run of defeats but managed to overcome the Saudis at Craven Cottage, despite conceding twice in the second half.
Australia sprinted into a 2-0 lead through Tim Cahill and captain Mile Jedinak but had to endure a nervous finale, as debutant Bailey Wright scored for the Socceroos between strikes from Hassan Muath and Taisir Al Jassim for the Middle East-based team.
The display, however, raised more questions than it answered for Australia, as they struggled to create against a woeful Saudi back four, while defensive lapses again cost the Socceroos goals.
Coach Ange Postecoglou made four changes to the starting XI that lost to Belgium in Liege on Thursday with Wright making his Socceroos debut in central defence, while Massimo Luongo earned his maiden start.
Midfielder Joshua Brillante and goalkeeper Mitch Langerak were also promoted, while Mark Bresciano, Trent Sainsbury, Mark Milligan and Mat Ryan sat on the bench.
After a shaky start where they conceded two free-kicks in as many minutes, Australia hit the front with their first attack, Cahill spreading the play on the counter-attack to Tommy Oar start the move.
Oar then found Mathew Leckie in the box but the FC Ingolstadt forward couldn't score and neither could Luongo before Cahill bundled the ball into the net from less than a metre.
It was 2-0 just four minutes later with Jedinak rising unmarked to nod Brillante's free-kick home, less than a minute after Alex Wilkinson was subbed off with a strained gluteal muscle, replaced by Sainsbury.
While the scoreboard looked promising, the performance was less so, with the Socceroos struggling to hold onto the ball early and failing to find new routes to goal.
Cahill's goal was his seventh in the Postecoglou era, while Jedinak was maintaining his record as the only other player to have scored in green and gold under the former Brisbane Roar and Melbourne Victory coach.
Otherwise it appeared that complacency had infiltrated Postecoglou's side with sloppy passes, particularly in Australia's defensive half, letting Saudi Arabia back into the match.
Sainsbury and Jedinak were arguably the main culprits, while the Socceroos struggled for cohesion amongst the front four of Oar, Leckie, Cahill and Luongo, although the latter again showed he has a bright future with some impressive moments.
Australia failed to test Saudi goalkeeper Waleed Abdullah after Jedinak's goal, although the Socceroos' skipper and Cahill both sent efforts wide of the mark, while Saudi Arabia tried a couple of long-range drives that did not trouble Langerak.
Postecoglou's men started the second half brightly but should have conceded in the 49th minute, only for the unmarked Yasir Al Shahrani to spray his shot wide from the edge of the six-yard box.
The Socceroos looked much more poised in possession up until the hour mark, although they did not create much, with their best move seeing Leckie chip to a surging Luongo, who could not keep his header down.
Saudi Arabia got back into the contest in the 70th minute with Langerak conceding a penalty on Mukhtar Fallatah, after the ball fell fortuitously to the substitute forward.
Langerak was lucky to stay on the pitch before Muath converted from the spot and suddenly the Saudis looked inspired.
The Socceroos restored their two-goal cushion just seven minutes later when Wright scored, after Saudi Arabia failed to clear an Australian set-piece, but the Gulf nation scored again soon after, with Al Shahrani teeing up Al Jassim, who took advantage of some lax marking from the Socceroos.
Australia held on, however, claiming just their second victory under Postecoglou's tutelage.
