Stamkos, who scored in the third period, has 21 points (nine goals, 12 assists) during the streak. He had an 18-game point streak in 2009-10, the longest in Lightning history.
Nikita Kucherov had three assists, and Brayden Point scored for the fourth straight game for Tampa Bay (18-9-1), which has won four of its past five games. Andrei Vasilevskiy made 36 saves.
"It was a weird game," Lightning coach Jon Cooper said. "[Seattle] is a heck of a team. I think they still carry that expansion mantra with them a little bit, but they certainly don't play like that. It was obviously a closer game than the score indicated."