Blackwood made 14 saves in the second, including against former Devils forward Kyle Palmieri in front at 14:35.
Dawson Mercer made it 3-0 at 5:46 of the third period when he took a pass from Andreas Johnsson at the New York blue line and scored on his backhand.
"Mercer's very confident with the puck. We feel very confident about what he's doing," Ruff said of the 20-year-old forward. "Some young players wouldn't dare try (what he's doing), but his ability to get in tight places, win battles, have a good stick, and work his way out has been a great asset for us."
Hamilton, who missed the previous three games with a lower-body injury, scored on a slap shot from the right face-off circle at 16:33 for the 4-0 final.
"[Hamilton] skates really well, is confident with the puck, and has a lot of poise," Blackwood said. "I think the presence that he brings on the back end, and the way he controls and puck, just really settles the team down on the power play and he gives our players a lot of confidence."
NOTES: Palmieri had four shots and was minus-3 in his first game at Prudential Center since the Devils traded him to the Islanders on April 7. He played six seasons with New Jersey. … Barzal had four shots and played 18:29 in the center's 300th NHL game. … New York played the 11th of 13 straight road games to begin the season. It faces the Tampa Bay Lightning on Monday and the Florida Panthers on Tuesday before its home opener, the first game at UBS Arena, against the Calgary Flames on Nov. 20. ... Hamilton had five shots and five blocked shots. ... Defenseman Ryan Graves led the Devils with 23:06 of ice time and had four blocked shots. ... Kuokkanen's goal was New Jersey's second shorthanded goal this season, which ranks second in the NHL behind the St. Louis Blues (three).