Stamkos tied it 2-2 with a power-play goal at 14:17 of the second, scoring with a one-timer from the bottom of the left circle off another pass from Kucherov.
Cirelli put Tampa Bay ahead 3-2 at 5:40 of the third period when he buried the rebound of Hagel's shot with his backhand.
"I thought we worked hard for two periods, and they found a way to get a little momentum there early in the third. Scored two big goals and took the lead on us," Blue Jackets forward Johnny Gaudreau said. "I thought we did a good job and we worked hard in their offensive zone. We had some good looks throughout the game but ended up losing."
Stamkos scored 16 seconds later with a one-timer from the high slot to make it 4-2 at 5:56. He then completed the hat trick with an empty-net goal at 17:57 for the 5-2 final.
"It was one of those games where, maybe this time of the year, it lacked a little emotion," Stamkos said. "I thought we kind of went through the motions in the first and the second. ... (A) little spark in the third. We needed that and we talked about it."
Kucherov leads the NHL with 139 points this season, including 96 assists, which is second in the League behind Connor McDavid (99). Only three players have ever had at least 100 assists in a season: Wayne Gretzky (11 times), Mario Lemieux (1988-89) and Bobby Orr (1970-71).
"I think it's a rarity in this league. Only three players have done it, and there's a chance that two guys might do it in the same season," Cooper said. "That's pretty remarkable. There's still a ways to go here. Hopefully it happens for him. We're all pulling for him."
NOTES: Kucherov has 16 points (two goals, 14 assists) during a seven-game point streak. ... Blue Jackets forward Alexander Nylander was a late scratch because of a lower-body injury, and forward Carson Meyer left the game in the first period because of an upper-body injury. ... Vasilevskiy won his 30th game, the seventh straight season he's reached the mark. ... Marchenko has scored five goals in his past six games. ... Cirelli has an NHL career-high 20 goals this season.