Richella Heekin saved for two years for a surprise Â£1,200 holiday for boyfriend Ben Marlow's 30th birthday last month.
But the excited couple arrived to find the airline's desk closed.
Staff confirmed the BHM airport code on their tickets meant Birmingham Alabama, not the UK's second city.
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The airport code for the British Birmingham is BHX.
"Richella's face has just gone red and she's in tears," said Mr Marlow.
"I was like - we're not going to Vegas then.
"I was more gutted for Richella than myself because it was a surprise."
Ms Heekin revealed the surprise to her boyfriend at a party in front of family and friends, with those who knew they were due to head to the US giving dollars as a present.
But the couple, from Sutton Coldfield and both carers for children with special needs, were devastated when they turned up to see no flights on the board.
The couple thought they were flying from Birmingham - in the West Midlands  - to Dallas and on to Las Vegas.
"I looked at the departure board and there's no flights," 26-year-old Ms Heekin said.
She said the error occurred after she spent time "doing a lot of clicking" on lastminute.com searching for flights, dates, prices and hotels.
"When I got my confirmation, I was checking my email. I checked the times and the code [BHM] was there," she said.
Ms Heekin said they contacted the website when at the airport, but the company said there was nothing that could be done.
Frustrated and with time booked off work, the couple used a new credit card to buy two late flights to Amsterdam instead - exchanging the gifted dollars for euros.
Lastminute.com said although it was not its error, the firm tried to find them alternative flights and contacted the airline and hotel for a refund, but one could not be provided.
Since attracting media attention, the couple have been offered a free five-day holiday to Las Vegas by Virgin Holidays.
A woman booked a dream holiday to Las Vegas, only to discover when she and her boyfriend arrived at Birmingham Airport she had mistakenly booked to fly from Birmingham Alabama.