A former graduate student at M.I.T. has pleaded guilty to killing a Yale graduate student in January 2021 in a gruesome shooting that shocked people on both university campuses.

The defendant, Qinxuan Pan, 32, narrowly escaped arrest just minutes after the murder. He spent the next three months hiding from law enforcement, and the following two years maintaining his innocence. That changed on Thursday, when Mr. Pan pleaded guilty, possibly bringing an end to a case that had caused some Connecticut residents to question the competence of local police.

Mr. Pan faces a single charge of murder, according to a statement by John P. Doyle Jr., the state’s attorney in New Haven. As part of his plea agreement, Mr. Pan could face 35 years in prison. He is scheduled to be sentenced on April 25.

The prosecutor’s office made no mention of Mr. Pan’s possible motives for the attack. In a 96-page warrant filed in state court in February 2021, a New Haven police detective described Mr. Pan’s actions as follows:

In 2019, when he was a doctoral student in M.I.T. ’s department of electrical engineering and computer science, Mr. Pan met Zion Perry, an undergraduate student at M.I.T., and they became friends. The two remained in contact through Facebook, where Ms. Perry posted an announcement celebrating her engagement on Jan. 30, 2021, to Kevin Jiang, a 26-year-old graduate student in environmental science at Yale.

A week later, on Feb. 6, 2021, Mr. Pan allegedly stole a dark blue S.U.V. from a dealership in Massachusetts, according to a criminal complaint filed by the police department in Mansfield, outside Boston. He drove to Ms. Perry’s neighborhood in New Haven, near the campus of Yale, where she was a doctoral student in biochemistry and biophysics.

Mr. Jiang and Ms. Perry had spent much of the day together. They went ice-fishing and cooked dinner at her apartment. He left a few minutes after 8 p.m., and climbed into his Toyota Prius. He had driven only a few blocks before Mr. Pan rammed him with the stolen S.U.V., according to the warrant. Mr. Jiang got out of his car, and Mr. Pan fired eight bullets at him, including multiple shots to his face.

A surveillance camera captured the crash. A neighbor witnessed the shooting, and multiple people saw the shooter get back into his S.U.V. and drive away, according to the police.

About 30 minutes after the shooting, police in the nearby town of North Haven received a call from a local scrapyard, where a driver had gotten his S.U.V. stuck on some railroad tracks. Police officers responded to find Mr. Pan behind the wheel of the dark blue GMC. He was wearing a gray knit hat printed with a “MetroPCS” logo, the detective noticed.

Mr. Pan told the officers he had become lost looking for the highway back to Massachusetts. The officers discovered that the vehicle’s license plate had been reported lost or stolen. In a statement to The New Haven Independent, a local news website, North Haven Police Chief Kevin Glenn said the officers did not know at the time that the vehicle had been stolen.

The officers did not take Mr. Pan into custody. Instead, they arranged for a tow truck, which retrieved the S.U.V. from the tracks, and brought Mr. Pan to a nearby motel.

Ninety minutes later, the New Haven Police Department issued an alert for a dark-colored S.U.V. In the alert, a dispatcher erroneously said the vehicle may have been driven by two people, possibly including a Black man. None of the witnesses to the shooting had reported a second assailant, and none had described the shooter as Black, according to the warrant.

The next morning, the same police officer who had discovered Mr. Pan stranded in the scrapyard was called to an Arby’s restaurant next door to the motel, according to the warrant. A worker had called because a bag had been discovered near the restaurant’s dumpster. It contained items including a Ruger semiautomatic pistol, seven firearm magazines and several boxes of ammunition.

The bag also contained a gray knit hat with a “MetroPCS” logo. Police requested a warrant for Mr. Pan’s arrest on Feb. 26, 2021.

A multistate manhunt ensued. Eventually, Mr. Pan was tracked to Alabama, where he had rented an apartment under an assumed name. After a three-month search, he was arrested in Alabama and extradited to Connecticut, Mr. Doyle said on Thursday.

During Mr. Pan’s prolonged flight, some residents in the New Haven area accused the police of having botched the case, according to The New Haven Independent. The fact that Mr. Pan was discovered stuck on railroad tracks should have prompted the officers to ask more questions, some residents said.

In a statement to The Independent, Chief Glenn said, “The officers involved in this investigation did their job properly.”