Brayden Point extended the lead to a 3-1 at 10:48 of the second when he poked the puck past Smith from in close.
Hyman cut it to 4-2 at 17:12, beating Vasilevskiy on a breakaway with the backhand.
McDavid's second goal made it 4-3 at 9:39 of the third period, but Kucherov scored an empty-net goal at 19:56 for the 5-3 final.
"It was an excellent hockey game and there were chances both ways," Woodcroft said. "We hit a post at the end of the game that could have tied it up. But the compete and effort on our team's part was there. One bounce here or there. It didn't go our way tonight."
NOTES:Perry has scored 14 goals with the Lightning, nine with the Montreal Canadiens, five with the Dallas Stars and 372 with the Anaheim Ducks. … Hyman has scored eight points (five goals, three assists) in a five-game point streak. ... Point has scored six points (three goals, three assists) during a five-game point streak. ... Oilers forward Ryan Nugent-Hopkins played in his 700th NHL game. He had five shots on goal and was minus-3. ... McDavid has scored a goal in six straight road games. … The game featured the past five Art Ross Trophy winners, given to the NHL scoring leader (McDavid, 2016-17, 2017-18 and 2020-21; Draisaitl, 2019-20; Kucherov, 2018-19). The last game to feature the previous five winners was Game 5 of the 2001 Eastern Conference Final, when the New Jersey Devils defeated the Pittsburgh Penguins, who had forwards Jaromir Jagr (1997-98, 1998-99, 1999-00 and 2000-01) and Mario Lemieux (1996-97).