Oman were leading the second leg 2-0 and 4-0 on aggregate.
A Reuters photographer at the match said that, despite a heavy police presence, Myanmar fans turned unruly when Japanese referee Ryuji Sato awarded a penalty to Oman with the home side trailing 1-0 and staring at early elimination from Asian qualifying for the 2014 finals in Brazil.
Oman's Ismail al Ajmi converted the spot kick to put his side 2-0 ahead after 39 minutes, sparking anger among the crowd at the Thuwunna Stadium and prompting players to flee for cover in the dressing room.
Fans leaving the stadium said the referee had made a bad decision in awarding the penalty.
Football is popular in Myanmar and its league is growing fast, but hooliganism is rare.
Myanmar's football association president Zaw Zaw tried to calm the fans at the stadium and said he would try to find out whether the game would be replayed or Oman would be awarded the victory.
Singapore beat arch-rivals Malaysia 6-4 on aggregate to reach the third round of the Asian World Cup qualifiers on Thursday after a tense 1-1 away draw while regional heavyweights Iran and Saudi Arabia cruised through.
The trio, and the 12 other second round winners on Thursday, joined Australia, South Korea, Japan, North Korea and Bahrain in the hat for the third round, a group stage featuring five pools of four teams, to be drawn in Brazil on Saturday.
Malaysian fans had turned out in force at the National Stadium in Bukit Jalil with 85,000, filling seats, aisles and gangways in a desperate bid to catch a glimpse of the eagerly anticipated causeway derby.
The game sprang to life in the 58th minute when Malaysian striker Safee Sali opened the scoring in controversial circumstances after the referee appeared to signal for a free-kick to the visitors only to then wave play on and allow the home side to score.
Singapore manager Raddy Avramovic had to be restrained on the sidelines as he protested in vain to the referee but just 15 minutes later the visitors were level after Shi Jiayi fired home to kill the tie and silence the vociferous home support.
The final minutes were played out with water bottles being thrown from the crowd towards the pitch as home fans became incensed at what they felt was timewasting by the Singaporeans, who suffered a number of injuries in the final 15 mimutes.
"That was a real poor referee," Avramovic told reporters after his players threw him into the air in celebration of result. "I really don't understand some decisions.
"It was a great atmosphere. We got what we came for."
Elsewhere, former Dutch international Frank Rijkaard had another easy night in charge of Saudi Arabia as the four times finalists routed lowly Hong Kong 5-0 away for an 8-0 aggregate win.
Iran coach Carlos Queiroz, who faced Rijkaard in an el clasico when the Portuguese was in charge of Real Madrid and the Dutchman Barcelona, was also celebrating after Team Melli's 1-0 win in the Maldives completed a 5-0 aggregate.
Also advancing were Indonesia, who perhaps could count themselves fortunate they were allowed to play after escaping a FIFA ban following a chaotic election of a new chairman of their Football Association.
Indonesia, who also sacked their Austrian coach Alfred Riedl just before the first leg of their tie with Turkmenistan, had Uruguayan born striker Cristian Gonzales to thank after he scored twice in a 4-3 win in front of 60,000 fans in Jakarta for a 5-4 aggregate win.
Qatar, hosts of the World Cup in 2022, proved they are a long way off the standard required to compete in the finals after falling to a 2-1 loss in Hanoi to Vietnam. Despite the defeat, the Gulf side advanced to the third round 4-1 on aggregate.
Gulf Cup champions Kuwait endured some nervy moments in Manila after falling a goal behind to Philippines but second half strikes from Yousef Naser and Waleed Jumah helped them win 2-1 on the night and 5-1 on aggregate.
India and United Arab Emirates survived attrocious conditions to complete their tie with the Gulf side claiming a 2-2 draw to advance 5-2 on aggregate.
The pitch at the Ambedkar stadium resembled a swimming pool after heavy rains lashed the field in New Delhi with the ball not rolling along the ground making passing impossible.
Also claiming a 2-2 draw to advance were Thailand who edged out Palestine 3-2 on aggregate.
The second round of Asian qualifiers provided some mismatches with Jordan enjoying their climb up the Himalayas to claim a 1-1 away draw in Nepal to complete an easy 10-1 win over the two legs.
Uzbekistan won 3-0 against Kyrgyzstan thanks to two goals from substitute Bahodir Nasimov for a 7-0 aggregate win.
But it was China, whose only World Cup finals appearance came in 2002, who were the biggest second round winners, hammering Laos 6-1 away to advance with a 13-3 aggregate.
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