Florida goaltender Sergei Bobrovsky stopped 28 shots while Matthew Tkachuk added a goal for the Panthers, who took the best-of-seven series 4-2.
"It's incredible," Florida's Brad Marchand said after the decisive Game 6.
"It's a feeling you can't really describe... words can't put this into reality, how great it feels. Such an incredible group."
After claiming their first crown last year, the Panthers became the first NHL club since Tampa Bay in 2020-21 to win back-to-back titles.
Florida beat Edmonton in seven games in last year's Stanley Cup final after squandering a 3-0 series lead, but this time dominated the last two games to hoist the trophy again.
"It's an amazing feeling," Bobrovsky said. "They are amazing, the group. I'm so privileged to be their goalie.
"It's a dream come true, and to win that trophy twice, it's amazing."
Not since Montreal beat Boston in 1977 and 1978 had a team defeated the same foe in the final two years in a row.
The Panthers, who also lost to Vegas in the 2023 final, obtained Tkachuk in a 2022 trade with Calgary and haven't missed the final since.
"We're a dynasty," Tkachuk said. "And I can't believe this is what has happened... It just shows how unbelievable the group is, the depth."
Reinhart became only the fourth player to score seven goals in an NHL Final after Jean Beliveau in 1956, Mike Bossy in 1982 and Wayne Gretzky in 1985.
"It's not easy coming back again," Reinhart said. "You know how hard it is to do. Sometimes that benefits you, and sometimes it doesn't.
"We just stuck with it. A lot has to go your way to be standing here at the end. We were up to task again."
Florida players took turns skating a lap on the ice after the game with the trophy lifted above their heads.
Florida centre Sam Bennett, who scored five goals in the final, won the Conn Smythe Trophy as the Most Valuable Player of the Stanley Cup playoffs.
"It's incredible," Bennett said. "This was harder than last time. We put in so much work. There are 25 MVPs in this group. It's the best feeling in the world."
The Oilers, seeking their sixth crown overall, have not won the Cup since 1990.
No Canadian team has won the Stanley Cup since Montreal in 1993.
Marchand, obtained in a trade from Boston, where he won a Cup in 2011, scored six goals in the Stanley Cup Final.
"We just had that fire," Marchand said. "We knew we had something special."
Florida became only the eighth NHL team to clinch the Cup on home ice in back-to-back seasons, the first since the Oilers in 1987 and 1988.