It’s one “L” of a plot twist.

Gov. Andrew Cuomo on Thursday unveiled a surprise, 11th-hour plan to fix the decrepit L-train tunnel linking Manhattan and Brooklyn while maintaining 24/7 service — and dodging the dreaded 15-month total shutdown.

Cuomo and a team of Ivy League engineers cooked up what they pitched as a “highly innovative” plan never before used for US railways that they claimed would be comparable in duration and cost to the original proposal — all without stranding commuters on both sides of the East River.

“The simple fact is you have roughly 250,000 people who are going to need another way to work,” Cuomo said at a press briefing, giving voice to what the MTA has known — and commuters have been bracing for — for years. “A closure of 15 months was highly problematic.”

Despite his optimism, some MTA board members cautioned that they needed to see the full plans before they could decide whether they would vote for them.

“If New York City residents can be saved a lot of aggravation, that’s a good thing, but there’s still a lot that needs to be looked at by the engineers, the contractors and the MTA board,” said board member Carl Weisbrod, a Mayor de Blasio appointee.

“Ultimately, it depends on what can be done and if it can be done safely and expeditiously.”

The first step in the supposed cure-all is to triage the crumbling Canarsie Tunnel, eaten away in spots by saltwater dumped by Hurricane Sandy — damage Cuomo and his team saw firsthand during a tour of the tunnel less than a month ago.

Workers will determine which sections of its concrete service walkway — or “bench wall” — need to be demolished and replaced and which can be salvaged and patched with a fiber-reinforced polymer, said Mary Boyce, dean of Columbia University’s Fu Foundation School of Engineering and Applied Science.

The original shutdown plan, which was slated to start April 27, called for the entirety of the tunnel’s bench walls to be torn down and rebuilt.

Once the bench walls are evaluated and repaired where necessary, the power cables embedded within them will be shut down.

A fiberglass barrier will then be erected between the tracks and the bench wall — effectively forming a tunnel within the tunnel — as an additional layer of protection against any future damage to the tunnel.

An entirely new network of cables jacketed with fireproof material will then be “racked” along — rather than embedded in — the fiberglass walls, allowing for easier access by maintenance workers.

This set-up would be a first for the nation, Cuomo said, but has been proven in transit systems in London, Hong Kong and Riyadh, Saudi Arabia.

The final addition to the tunnel itself is a system of smart sensors capable of detecting even minute fluctuations in the structural integrity of the bench walls.

The sensors will communicate electronically with trains passing through the tunnels, providing the MTA with rolling updates on any further decay in the century-old tunnel behind the fiberglass.

“This could be a national model because it is a totally different way to reconstruct a tunnel,” Cuomo said.

Boyce added that, if successful, the design could be used for other city projects including Phase 2 of the Second Avenue tunnel.

Throughout the piecemeal project, L trains will run unimpeded during weekdays and spaced about 15 to 20 minutes apart on nights and weekends, said acting MTA Chairman Fernando Ferrer, who crowed, “No L-pocalypse!”

Despite one of the tunnel’s two tubes remaining in service at all times, the project will still be completed in 15 to 20 months — or potentially as quickly as the timeline for the shutdown, Ferrer said.

Pressed to promise that the overhaul would take no longer than 20 months, Cuomo refused.

He also declined to put an exact price tag on the plan but insisted that the already-inked $492 million contract with Judlau Construction Corp. would stand.

“We believe it can be done within the envelope” of that cost, Cuomo said, while also floating that the contract could even be reworked because “less time, less money.”

City officials were mostly blindsided by the about-face, with only a small circle informed of the plan in a highly secretive Wednesday meeting, insiders familiar with the huddle told The Post.

City Councilwoman Carlina Rivera (D), whose district includes the Manhattan side of the tunnel, also called for hearings on the plan changes.

“Today’s news was announced without warning and with nowhere near enough detail, after years of careful planning by the communities,” she said.

De Blasio spokesman Eric Phillips said, “So long as this new strategy proves to be real, the mayor thinks this is great news for L-train riders.”

NYC Transit President Andy Byford called the plan democracy in action, but John Raskin, executive director of the transit-advocacy group Riders Alliance, wasn’t convinced.

“The governor’s plan may or may not work, but you’ll pardon transit riders for being skeptical that a last-minute Hail Mary idea cooked up over Christmas is better than what the MTA came up with over three years of extensive public input,” he said.