Kane, brought in to add balance to a star-laden offense that features Connor McDavid and Leon Draisaitl but has struggled with its depth, scored 11:21 into his first period as an Oiler, redirecting Evan Bouchard's shot from the point.
Edmonton scored three in less than two minutes during the first, and scored first for the first time in 12 games en route to its fourth straight victory.
"It's nice to contribute on a new team coming in, you want to show what you can do," said Kane, who signed Thursday and was introduced to the Edmonton media Friday. "Obviously, it was great to get the boys on the board early. And everyone kind of took off after that."
Zach Hyman and Draisaitl each had two goals and Ryan Nugent-Hopkins and Derek Ryan also scored for Edmonton. Hyman and Nugent-Hopkins had an assist apiece, while Duncan Keith and Warren Foegele each had two assists. Stuart Skinner made 21 saves for the road team.
"All four lines contributed and that was great to see," Kane said. "It made it easy for our team to roll lines and keep our foot on the gas."
Edmonton is the fourth franchise for the 30-year-old forward whose contract was dumped by the San Jose Sharks amid myriad issues. As the Oilers continue the season, and battle for the postseason, there will be questions about his past, from suspensions due to violations of COVID-19 protocols, a bankruptcy and a gambling addiction. But for one night, at least, the focus was on hockey.
"When you get onto the ice, you can kind of put everything else to bed," Kane said. "And hopefully that continues."
Josh Anderson and Tyler Toffoli scored for Montreal in its fifth straight loss. Sam Montembeault allowed six goals on 16 shots before being pulled after two periods. Cayden Primeau had seven saves in the third.
Kane, a two-time 30-goal scorer who has had at least 20 in a season five other times, will likely be used in several different line combinations while Edmonton searches for the right fit. After starting the season with five straight wins, the Oilers began Saturday night on the outside of the Western Conference playoff picture.
"When a new player comes in, they press, they want to make sure they contribute to their new team, and it's great for him to jump in and get one early," Edmonton coach Dave Tippett said. "He looks in decent shape. You can tell he's rusty, hasn't played in a while, and he has to get up to speed a little bit. But it's good to get him up and get him in the lineup."
The Associated Press contributed to this report.