A 28-year-old woman from Campbell whose car tumbled hundreds of feet down an embankment on Mount Hamilton east of San Jose was rescued and taken to a hospital Tuesday morning after she spent more than 12 hours stuck and injured, officials said.

In the end, police said, the search for where the car crashed was both complicated and aided by location-based technology.

On Monday afternoon, just after 2 p.m., Campbell police officers received a report from General Motors’ OnStar system saying there had been a rollover accident involving Melissa Vasquez’s Chevrolet Cruze in the area of White Oaks Road and Shelley Avenue in Campbell, said Capt. Gary Berg.

That was just a couple of blocks from the woman’s home.

Officers spent two hours searching the area, Berg said. But the pegged location wasn’t right. Police had OnStar honk the car horn remotely, to no avail. A second strategy — having officers run sirens in different locations to see if they could be heard over the OnStar system — also failed.

A knock on Vasquez’s door got no response. And the car wasn’t there.

Officers then contacted Vasquez’s cell company, which provided a location of her phone within a 7-mile radius of downtown San Jose, Berg said. Authorities were still unable to locate the car. Campbell police officers broadcast the vehicle’s description to all agencies in the county, he said.

Then, just before 3 a.m. Tuesday, Campbell police officers received a missing person’s report from Vasquez’s stepmother, with whom she lives, officials said. She said she hadn’t heard from her.

Officer Dave Cameron met with the stepmother and asked if Vasquez had Find My iPhone, an app that allows you to locate your misplaced iPhone using cell signals. The stepmother responded that Vasquez owned an iPad — but she didn’t know where it was.

So Cameron called the cell company, which could tell the iPad was in the Campbell home. Soon, the stepmother found the tablet computer — but it was locked.

“So I made an educated guess, based on a series of common numbers people use for passwords,” Cameron told reporters. Cameron is a SWAT team member and accident reconstruction specialist but acknowledged that he’s known within the department as “kind of a tech geek.”

“Amazingly, Officer Cameron was able to guess the correct password after only 3-4 tries using his knowledge of commonly used password combinations,” officials said.

The Find my iPhone app was also locked. But the same password opened it up. Cameron activated the “lost phone” feature and saw a map of the location of Vasquez’s iPhone — 14555 Mount Hamilton Rd.

“It gave a very small search area,” Cameron said. He noticed that Vasquez’s cell phone only had 12 percent battery life left.

“You think about it. If we didn’t have that specific location I would hate to think what the outcome would be without him logging into that account,” Berg said.

Officers from San Jose and deputies from Santa Clara County responded to the area soon after receiving the information from Campbell police.

Less than 20 minutes later, at around 5:30 a.m., officers located Vasquez on Mount Hamilton. The car, which had plummeted about 500 yards off an embankment, was on its roof, said California Highway Patrol Officer Ross Lee. The victim was outside the car, face-down but conscious.

A U.S. Coast Guard helicopter responded and airlifted Vasquez to Regional Medical Center of San Jose with major injuries, including to her abdomen and legs. She is expected to survive, Ross said. Relieved family members met with Vasquez at the hospital and thanked rescuers.

General Motors said in a statement Tuesday that it was looking into what happened with the OnStar system and was “saddened by this incident involving one of our subscribers.”

“Our subscribers’ safety and security is OnStar’s utmost concern. We are currently conducting a complete investigation, including information we have received from our call centers, our cellular network provider, our engineering team and the local authorities to better understand what occurred,” the company said.

Cameron said he was heartened that the technology that was available helped save Vasquez.

“Sixteen years ago, that wouldn’t have happened,” he said. “It would have been phone calls and guesses and maps.”

Chronicle staff writers Henry K. Lee and Demian Bulwa contributed to this blog post.