Alex DeBrincat, Kirby Dach and Dominik Kubalik scored, and Patrick Kane and Tyler Johnson each had two assists for the Blackhawks, who were coming off a 4-2 loss at the Colorado Avalanche in their opener on Wednesday. Lankinen made 25 saves.
"I thought we had stretches in the game where we were really good, like some of the second period," Chicago coach Jeremy Colliton said. "I felt like we were close to taking over. I think ultimately, we just have to find a way to be more consistent shift to shift so we can build momentum."
Dach cut it to 3-2 at 16:07 of the third. The Blackhawks pulled Lankinen while on a power play for a 6-on-4 advantage, and Dach was able to get the rebound of Kane's initial shot and score from the right post.
Lankinen was then pulled again for an extra attacker, and following a scramble in the Devils zone, Kubalik tied it 3-3 on a shot from the right face-off circle with 26 seconds remaining.
"You want to win, so nice to come from behind … but [when] we lose those even in overtime, they don't feel good," Blackhawks captain Jonathan Toews said. "We just have to make sure we're not giving up too much offense, too easy."
Hamilton, a defenseman who signed a seven-year, $63 million contract on July 28, scored from the high slot 17 seconds into the game to give the Devils a 1-0 lead.
"It was a great pass (by Pavel Zacha)," Hamilton said. "It wasn't my best shot, but a good screen, I think. I'm obviously happy it went in."
The goal was the fastest to start a season in New Jersey history. The previous record was set by Zach Parise, who scored 26 seconds into a 4-0 win at the Carolina Hurricanes on Oct. 10, 2006.
"It couldn't have been a better start for [Hamilton]," Devils coach Lindy Ruff said. "We know what he can bring, we know what he can add, and to get involved offensively right off the bat was great for our team."
DeBrincat scored 51 seconds into the second period with a one-timer from below the left circle on the power play to tie it 1-1, but Hughes gave the Devils a 2-1 lead on a spinning wrist shot from the left circle at 17:58 of the second.
"[Hughes] wants to build off of where he was last year and he wants to get better every day," Ruff said. "I think there's still a lot to learn and he's got tremendous talent. He wants to hit his next level."