Lee got the Islanders to within 3-1 at 13:44 of the third period, scoring from the top of the crease with Sorokin pulled for an extra skater.
Nelson cut it to 3-2 at 17:25 with a power-play goal from the right face-off circle with Sorokin again on the bench for an extra skater.
Tampa Bay was 4-for-5 on the penalty kill.
"I thought that we played pretty well," Lightning coach Jon Cooper said. "We took too many penalties, and it cost us. I liked our compete. … We can't take the penalties that we took."
Glendening scored an empty-net goal with 30 seconds remaining for the 4-2 final.
NOTES: Kucherov had at least three points for the 15th time this season. He leads the NHL with 98 points (37 goals, 61 assists). … Lightning defenseman Erik Cernak played after missing a 5-3 loss to the Washington Capitals on Thursday because of an illness. He had one shot on goal in 21:10 of ice time. … Islanders forward Casey Cizikas returned after missing a 4-0 loss to the St. Louis Blues on Thursday because of an upper-body injury. He had two shots on goal in 12:11 of ice time. … New York defenseman Scott Mayfield did not play and is day-to-day with a lower-body injury.