"As the game went on, we just didn't reset ourselves," Sharks captain Joe Pavelski said. "We kept missing passes and just fed their rush. They're good players, for sure. They made some plays, played with the puck a lot. And partly that's on us. Any time we had it we seemed to give it back to them."
Kucherov buried a wrist shot into the upper left corner of the net 44 seconds into the second to give Tampa Bay a 2-1 lead.
Koekkoek made it 3-1 at 9:21 when he scored on a backhand between Jones' pads from close range.
The Lightning extended their lead to 4-1 at 12:00 on Namestnikov's wrist shot. Stamkos took a cross-ice pass in the left circle from Kucherov and quickly sent the puck to Namestnikov on the other side.
Namestnikov scored a power play goal at 6:14 of the third period to make it 5-1.
"There was a lot said in between the first and second," said Lightning coach Jon Cooper, who got his 200th NHL victory. "We had seven shots on goal and we were passing up Grade-A chances. It's pretty clear that that wasn't working for us. They started getting after it a little bit in the second and it worked out."