Authorities, aided by technology, tips and luck, wrapped up a tension-filled weekend with the arrest Monday of a man suspected of setting off homemade bombs in New York and New Jersey that injured 29 people.

Ahmad Khan Rahami, a 28-year-old man and the target of an hourslong manhunt across the two states, was shot and injured in a gunbattle with police from Linden, N.J., where he was spotted sleeping outside a bar. Two police officers suffered minor injuries in the firefight.

Mr. Rahami, a naturalized U.S. citizen from Elizabeth, N.J., is suspected of planting bombs in four locations, beginning with an explosion Saturday morning near the starting line of a 5K race in Seaside Park, N.J. No one was hurt, but a blast that night in New York City injured 29 people. A third bomb found nearby failed to detonate, and five pipe bombs were found in an abandoned backpack Sunday by passersby near the train station in Elizabeth.

No motive has been cited by authorities who said Monday they were seeking any accomplices but believed Mr. Rahami had acted alone. The suspected bomber, shown after his arrest on TV strapped to a stretcher and loaded into an ambulance, was in surgery Monday. He was expected to recover from arm and leg wounds.

Prosecutors in New Jersey charged Mr. Rahami late Monday with the attempted murder of police officers in the shootout. Those charges are likely to keep him in custody while federal prosecutors in New York and New Jersey prepare terrorism charges.

Early Monday, alerts screeched, buzzed and flashed across mobile devices in the New York metropolitan area seeking the public’s help in tracking down Mr. Rahami. The message asked people to call 911 if they saw him.

The so-called Wireless Emergency Alert would emerge as an important part of the manhunt, along with surveillance video, fingerprint experts and the bomb squad.

“There was a lot of technology involved in this, but a lot of good old-fashioned police work, too,” said New York Police Commissioner James O’Neill, who is in his first week on the job.

One of the homemade bombs allegedly detonated by Mr. Rahami exploded Saturday night near a large metal trash bin in the Chelsea neighborhood of Manhattan. Officials suspect Mr. Rahami tried to place the bomb in a way that would turn the trash bin into a projectile.

Instead, they said, the metal absorbed much of the blast. The bomb was filled with ball bearings and other shrapnel, officials said. “He’s a very good bomb-maker,” one official said, “despite his mistakes.’’

After a similarly built bomb—made with a cellphone and a pressure cooker filled with shrapnel—was found four blocks away, police investigators said, they suspected a serial bomber, setting off an urgent chase.

An early break came from a surveillance video in the Chelsea neighborhood that showed a man wheeling a duffel bag and leaving it on the street. Soon after, two passersby spotted it and, apparently not realizing what was inside, emptied the contents—the bomb wrapped in a white garbage bag—and walked off with the duffel bag, officials said.

Police officials said that by removing the bomb, the two unidentified men may have accidentally disabled the device.

“Once they picked up the bag, they seemed incredulous,” said Robert Boyce, the New York Police Department’s chief of detectives. “It’s difficult to say right now if they…inadvertently perhaps, even pulled a wire.”

Officials said late Monday they still wanted to talk to the two men as witnesses.

Bomb squad experts worked until Sunday evening to render the device safe for examination. Once it was defused, the device provided clues that pointed to Mr. Rahami, authorities said, including a fingerprint that matched his. The cellphone meant to trigger the explosion was connected with Mr. Rahami’s family, authorities said.

With those clues, investigators sought Mr. Rahami for questioning. They believed he had been driving a black SUV that they found parked in Elizabeth. Agents quietly watched the vehicle and the surrounding homes, waiting to see if he surfaced, officials said.

Five people got into the car and drove off Sunday evening, officials said, and investigators followed. They stopped the car by the Verrazano Bridge and found two women in front and three men in back. None was Mr. Rahami.

After questioning the car’s occupants, officials from the Federal Bureau of Investigation and the NYPD became more convinced Mr. Rahami was their suspect, authorities said. They also came to believe that Mr. Rahami knew police were after him.

That night, investigators got lucky again. Two men found a backpack near the train station in Elizabeth, N.J., and decided to take it. As they walked away, they opened it and saw wires, officials said. They dropped the bag and called police.

Police used a robot to examine the package and one of the devices exploded, authorities said. No one was hurt. Investigators suspect Mr. Rahami abandoned the backpack while trying to avoid capture.

On Monday morning officials released Mr. Rahami’s name and picture to the public, pushing out a text alert to millions of cellphones.

Around 11 a.m., two friends in Linden noticed a man sleeping in the doorway of a bar on Elizabeth Street.

One of the men, who worked at the bar, said he thought the man, who was wearing a hoodie, looked like the suspect.

“That’s the guy that planted the bomb,”’ the bar worker told Jack Mazza, a 55-year-old mechanic who works around the corner

“No, it’s not,” Mr. Mazza said he replied. “You can’t even see his face. How do you know?”

The two men tried to wake the man and get him to move, but he cursed and told them he was sleeping, Mr. Mazza said.

Still unsure if the sleeping man was the suspect, they called police.

“A few minutes later the cops showed up, and the guy pulled out a gun and started shooting through the glass at them,” Mr. Mazza said in an interview. “Then he ran out and took off down Elizabeth Avenue. The cops were chasing him and he was shooting while he was running.”

Officials said Mr. Rahami pulled the weapon out of a fanny pack-type bag, similar to a bag worn by the man in the surveillance video.

“I guess he was trying to shoot the cops, but he was hitting passing cars,” Mr. Mazza said. “He could have hit us. He could have hit anyone.”

Linden Police Captain James Sarnicki said one officer was struck in his bullet-resistant vest, and another suffered cuts to his head from broken glass.

“I understand it was a walking gunbattle. He was walking and shooting off his gun indiscriminately,’’ Captain Sarnicki said. “Eventually, additional officers responded and returned fire and were able to take him down.”

— Mark Morales contributed to this article.

Write to Pervaiz Shallwani at pervaiz.shallwani@wsj.com and Devlin Barrett at devlin.barrett@wsj.com

Copyright ©2016 Dow Jones & Company, Inc. All Rights Reserved.

http://www.wsj.com/articles/manhunt-snares-new-york-city-bomb-suspect-1474332233