Late goals from Maximilian Hofmann and Yusuf Demir denied Dundalk their first Europa League point of the campaign as Rapid Vienna secured a 4-3 home win.
An 82nd-minute penalty from substitute David McMillan had looked to have earned a hard-fought 2-2 draw for the League of Ireland side.
Hofmann and Demir then struck before McMillan added another penalty.
Patrick Hoban gave Dundalk a seventh-minute lead, with Dejan Ljubicic and Kelvin Arase putting the hosts 2-1 up.
It was a third defeat from three Group B games for Filippo Giovagnoli’s men after they lost at home to Molde and away to Arsenal.
A goalkeeping error led to Dundalk taking the lead in the seventh minute after good build-up play down their right hand side through Sean Hoare and Sean Gannon.
The ball was played back to captain Chris Shields and his searching cross found Hoban, whose header squeezed past goalkeeper Paul Gatler, who looked set to make a save.
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