A fishing boat smashed head on into runway approach lights at La Guardia Airport early Sunday after the vessel’s drunken captain deserted the helm for a three-way sex romp — exposing a stunning security weakness, sources told The Post.

Police were unable to reach the boat to determine whether it was a threat for about 30 minutes, even though a Port Authority police vessel was tied up at a nearby dock.

There was no crew available to operate it because, in a money-saving move, the PA had decided to operate its navy only during daylight hours.

The PA Police Department finally had to call for help from the NYPD’s Harbor Unit.

If those on board the love boat had been “terrorists with bad intentions, they could have easily succeeded,’’ a PAPD official said.

“If they had hand-held rockets, they would have had plenty of time to fire at planes.’’

“There are no marine patrols at La Guardia and JFK on the afternoon and midnight tours,’’ a PAPD official said.

“These boats are integral to perimeter security.’’

Paul Nunziato, head of the PAPD union, was furious.

“The boats were purchased with federal money. They are not being deployed 24-7 — as the public would expect them to be,” he said.

The wild night began Saturday in a tavern in College Point, Queens, where boat owner Craig Gallo, 51, James Benenato, 60, and Mary Ann Belson, also 60, began chatting between drinks, another source said.

Neither of the two men had met Belson before.

Gallo, who lives in New Jersey and works for a financial company on Long Island, invited them aboard for a moonlight cruise. And before very long, the boat was rocking.

The joyride ended abruptly at the end of Runway 22, where the boat got impaled on a lighting stanchion.

Belson is being treated for a possible broken nose and jaw, and Gallo, who was later charged with operating a boat under the influence, suffered facial injuries. Benenato was not hurt.

They were lucky the boat was supported by the stanchion. Otherwise, the badly damaged craft might have sunk while they waited for help, the source said.

Before the wreck, “a consensual three-way sex endeavor was going on,’’ the source added.

“There’s a moral here: If you’re feeling amorous aboard a boat, I suggest you drop your anchor before you drop your pants.’’

The incident was the latest black mark against the PA, which is responsible for keeping unauthorized people off airport property.

In 2012, a jet-skier who had run aground at JFK Airport walked undetected across two runways and into a terminal despite motion detectors and security cameras on the grounds.

And in 2013, a man dressed as a woman hopped a fence at Newark Airport after a tryst in a car near the airport ended badly. At the time, a source revealed that perimeter cameras failed to detect the intruder.