Video shows the 24-year-olds initially enjoying themselves as they sunbathed and sped around in the water.
Londoner Frank, who is unable to swim, is shown looking shocked as he holds up part of the key, realising they are in trouble.
He tries to turn the part of the key that is stuck but is unable to get the engine going again.
At this point, Leah, from Cheshire, pans the camera around to show them in the middle of the sea.
The clip then ends as the sun appears to be setting.
Thankfully, with a bit of persistence, Frank was able to turn the tiny piece of key that was still in the ignition and drove back to the beach where boat staff were waiting.
Leah shared the video on TikTok two weeks ago, writing: “That time we rented a boat in Greece and the key snapped in the ignition when we were out at sea.”
The video has gained over 410,000 views and 30,000 likes, with many viewers shocked at the shock mishap.
One said: “His face with the key.”
Another wrote: “Nah, I’d pass away there and then, what the hell.”
A third commented: “Worst ever nightmare, I don’t know what I would have done.”
While another person joked: “Man thought about the fine instantly.”
Speaking today, Leah said: “We were stressed and scared because just as the key snapped then the sun seemed to disappear and the wind started to pick up.
“We were rocking a bit more and the boat was floating away because we didn’t have the anchor down.
“Oh and on top of that my boyfriend can’t swim, so he was stressed out.
“It must have been an old key, so when we went to turn it to start the boat again the key just snapped in half.
“The people that rent the boat to us were supposed to give us their number so in an emergency they can send out a rescue boat or someone to come and save us, but they must have been in a rush and they forgot to give us the number before we went.
“We literally had no idea what to do, as we were ages away from the beach where we got the boat from.
“There was no way I could’ve swam and suddenly there were no boats passing or near us.
“We had another number for another boat company which we tried to call but they weren’t answering the phone.
“In the video you can see how my boyfriend is putting the remaining part of the key back in the ignition to piece it together.
“I don’t know how he managed this, but after a while he managed to turn the broken bit in the ignition with the broken bit we had, so the engine started.
“We literally drove straight back and managed to make it back to the beach and they pulled us in.
“Surprisingly, we didn’t get a fine for breaking the key, they were really more concerned about us not calling them in an emergency, but we didn’t have their number.
“I have no idea how they turned the engine off because that key was stuck in there.”