Killorn made it 2-0 at 12:29 of the second with an unassisted goal on a shot from the slot, and Stamkos scored his 150th NHL power-play goal with 27 seconds left in the period to make it 3-0.
"We've had a tendency this year when we've had the lead to sit back a little too much," Stamkos said. "Our team is built to continue to press, use our speed, and then the skill takes over. We kept pouring on the goals. It was a great way to come out in the third period, score one early, and we just kept going."
Hedman scored his third goal in three games to give Tampa Bay a 4-0 lead 52 seconds into the third.
Johnson made it 5-0 at 3:51 with his second of the night.
"The third period was just unacceptable," Sharks coach Peter DeBoer said. "It was just poor effort. I think instead of sticking with it, I think we felt sorry for ourselves after that fourth goal. Maybe start thinking about tomorrow, but you can't do that in this league. So throw that one out."