A team made up of mostly expats from India and Pakistan, Oman chased down Ireland's total of 154-5 with two balls to spare after needing 14 runs off the last over.
It all went wrong for paceman Max Sorensen who served up two no-balls for bowling high full tosses as Ireland's hopes of making it to the main draw from Group A faded.
Bangladesh avoided Ireland's fate earlier in the day as the Asian test-playing nation staved off a spirited fightback from the Netherlands to kick off their campaign with a tight eight-run victory.
Fresh from their impressive Asia Cup show at home where they defeated Pakistan and Sri Lanka to reach the final, Bangladesh would have liked to prove they are a much better side than to be competing with the associates for a place in the Super 10 stage.
But impressive bowling from seamers Timm van der Gugten (3-21) and Paul van Meekeren (2-17) restricted Bangladesh after they were put in to bat and it was left to opener Tamim Iqbal to lift his team to 153-7 with an unbeaten 83.
Left-hander Tamim carried his bat through the innings, hitting six fours and three sixes in his 58-ball knock to notch up his fourth half-century in the shortest format of the game while all his batting colleagues struggled.
The Netherlands appeared well on course for an upset win until they lost their way by losing three quick wickets to finish on 145-7.
They were 112-3 in the 16th over but were reduced to 121-6 before Mudassar Bukhari and Pieter Seelaar smashed paceman Al-Amin Hossain for 16 in the penultimate over to keep Netherlands interested.
Fast bowler Taskin Ahmed bowled a tight final over to calm Bangladesh's nerves as their opponents failed to find the boundaries, needing 17 runs for victory.
Openers Zeeshan Maqsood and Khawar Ali gave Oman a blistering stand of 69 in 8.3 overs before both inside-edged medium pacer Kevin O'Brien on to their stumps.
Ireland underlined their superior experience of playing in ICC tournaments by reducing their opponents to 90-5 in 14 overs.
Although the sparse crowd at the picturesque stadium, with the Himalayas in the background, could not have envisaged what would follow, Aamer Ali and Jatiner Singh brought Oman back into the contest with a 47-run stand for the sixth wicket.
Ali hit 32 off 17 balls and was out in the final over with his team still needing four runs from two balls.
But it did not prove too damaging as Sorensen, unable to grip the greasy ball due to heavy dew on the ground, bowled a high full toss that went through the legs of the wicketkeeper for four, sparking wild celebrations among the Oman players.
Original source: #ICCWT20: Oman stun Ireland on debut