Sean Kuraly, Kent Johnson and Kirill Marchenko also scored, and James van Riemsdyk had two assists for the Blue Jackets (19-17-6), who have won three straight and six of eight. Elvis Merzlikins made 29 saves.
Mateychuk, 20, and Del Bel Belluz, 21, are part of the youth movement that has come through Cleveland of the American Hockey League.
“They’ve got swagger. They've got a confidence,” Columbus coach Dean Evason said. “Both guys that come up, they've got a ton of points down there, but they play the right way. It just sets them up to have success.
“The team, this group in particular, the most important thing to them is the two points. That's what's awesome about this group. Are we happy for people? One hundred percent. But the people that we're happy for are happy to win -- as opposed to just scoring a goal or making their debut or whatever -- it's that the Columbus Blue Jackets win.”
Eeli Tolvanen scored twice for the Kraken (17-22-3), who have lost four in a row. Philipp Grubauer allowed five goals on 19 shots before being replaced at 15:45 of the second period by Joey Daccord, who stopped all four shots he faced.
“I think the second period is embarrassing from us,” Tolvanen said. “We have to do something, get some life on the team. … We gave them all their goals. Sloppy D-zone turnovers.
“I feel like when we play a simple game, then we are at the best. Then when we start trying to make fancy plays, that's when we get scored on.”
Kuraly gave Columbus a 1-0 lead at 11:58 when he tipped a shot by Ivan Provorov for his first goal in 15 games.