The point lifted Australia to seven points in Asian zone Group B qualifying going into its final two qualifiers against Jordan - which trails Australia on goal difference - and Iraq later this month as it gets set to punch its ticket to Brazil.
The outcome suited Japan, which became the first nation to qualify for next year's World Cup.
Whiz-kid Oar pounced in the 81st minute, bursting down the left past a couple of challenges to curl in a looping cross which evaded the valiant effort of goalkeeper Eiji Kawashimi as it dipped into the net.
Deliberate - or otherwise - Oar's first goal for his country was a moment to cherish.
But joy turned to despair on the stroke of full-time when Matt McKay was penalised for handball as he moved to intercept a low cross and CSKA Moscow midfielder Keisuke Honda buried the spot kick to leave the Socceroos agonisingly just short of what would have been a famous win.
Australia played with patience and poise, mixing long balls in the direction of lone striker Tim Cahill, with playing out from the back.
Osieck's men were also biting in the tackle, restricting the space available for the Blue Samuari's purists to operate in as a yellow brick wall guarded the away goal.
The Socceroos also rode their luck in front of a 60,000 crowd baying for the home side to break the deadlock.
Osieck made five changes from the team that drew 2-2 with Oman in March.
As expected, Neill - suspended against Oman, and Sasa Ognenovski - dropped for that match - were reunited at the back as Osieck opted for experience.
J-League based striker Josh Kennedy - chasing his first Socceroos start in 17 months after battling back from injury - had to be content with a place on the bench, while Mile Jedinak, Alex Brosque and Michael Zullo missed out through injury.
That left Cahill - Australia's master of international rescue - to lead the line with Brett Holman tucking in behind, and Kruse on the right and Oar on the left, providing the width.
Japan coach Alberto Zaccheroni unleashed a full strength line up boasting all the big guns- Yuto Nagatomo, Yasuhito Endo, Shinji Kagawa and fellow midfield magician Honda.
And Endo had the chance to cause an alarm in the sixth minute, but his 25 metre free-kick drifted just wide after Ognenovski had been penalised for a foul on Shinji Okazaki.
Then in the 12th minute defender Maya Yashida wasted a free header from a Honda corner, much to Australia's relief.
Midfielder Endo then fired just over from the edge of the area before a neat build-up involving Kruse and Cahill saw Holman steer his shot wide at the other end when well placed.
Goalkeeper Mark Schwarzer rescued Australia in the 18th minute when a clever passing move orchestrated by Honda opened up the Socceroos up and it took a one-handed stop from the veteran No.1 to repel Kagawa.
Growing in stature as the game progressed, Australia might have broken the stalemate in the 34th minute when a raking through ball from Brett Homlan was latched on to by Kruse who was denied by the onrushing Kawashimi.
Japan threatened again early in the second half, Kagawa crossing deftly for Honda to prod just wide in the 54th minute.
Two minutes later Kagawa cut inside Luke Wilkshire and clipped a shot which grazed the post with Schwarzer beaten.
Osieck made his first change in the 72nd minute, with Holman giving way to Dario Vidosic.
Cahill was denied by a superb block from Yoshida after Kruse cut the ball back invitingly in the 75th minute in a rare burst forward by the visitor.
It took another great stop with Schwarzer to defy wideman Yuto Nagatomo 12 minutes from time. Then came Oar's memorable moment before Honda replied to send Japan to Brazil 2014.
Osieck admitted there was much disappointment in the Australian dressing-room following the draw, despite the result actually being a positive one in the context of the World Cup campaign.
But he declared himself pleased with the Socceroos' defensive discipline and how they stuck to the game-plan.
"When you are very close to winning such a very difficult game, then of course you are disappointed," coach Holger Osieck said.
"But I told my players they should have their heads up, not question themselves and I think we should gain a lot of confidence from this game to get ready for the two home games in Australia now."
Skipper Lucas Neill was thrilled with his side's defensive effort, though gutted to miss out on three points which would have gone a long way to ensuring their participation in Brazil.
"It feels like two points dropped, but I don't think too many people gave us a chance before the game. I did," Neill said.
"We possibly deserved three points and it would have set us up lovely. But we'll take the point, and we know we've got two games, and importantly destiny's still in our hands."
Socceroos XI: Mark Schwarzer, Luke Wilkshire, Lucas Neill, Sasa Ognenovski, Matt McKay; Robbie Kruse (Archie Thompson 90+3'), Mark Milligan, Mark, Bresciano, Tommy Oar, Brett Holman (Dario Vidosic 72'), Tim Cahill.
Japan XI: Elji Kawashima; Yuto Nagatomo, Maya Yoshida, Yasuyuki Konno, Atsuto Uchida (Mike Havenaar 86'); Yasuhito Endo, Makoto Hasebe; Shinji Kagawa, Keisuke Honda, Shiji Okazaki (Hiroshi Kiyotake 88'); Ryoichi Maeda (Yuzo Kurihara 80').How the match is trending:
Oman's 1-0 win over Iraq in Muscat saw it jump up to second on nine points - but it has played a game more than the Socceroos.
Ismail Al Aimi headed home on the stroke of half-time for the home side against a lacklustre Iraqi outfit.