Killorn had pair of in-close chances off a Stamkos feed earlier in overtime turned aside by Stars goalie Jake Oettinger.
“He made up for it … great shot,” Stamkos said.
Radek Faksa made it 4-4 with 4:42 left in the third period, picking up the Stars’ fourth short-handed goal after stealing the puck from Mikhail Sergachev deep in the Lightning zone. Tampa Bay has given up five short-handers.
Sergachev assisted on Killorn’s goal.
“Listen, nobody felt as bad as Sergy did,” Lightning coach Jon Cooper said. “I thought the attitude during that whole everything happened there was outstanding by the guys.”
Ian Cole gave Tampa Bay a 4-3 advantage 3:55 into the third on his first goal in 52 games.
Tampa Bay also got goals from Ross Colton and Nick Paul. Brian Elliott made 28 saves.
Joe Pavelski and Jason Robertson had a goal and an assist, and Mason Marchment also scored for the Stars. Oettinger stopped 33 shots.
“They’re not all going to look great and be perfect games, but found a way to get a point against a real good team,” Stars coach Pete DeBoer said. “The game went back and forth three or four times, so it was a good point.”
Robertson (nine goals, 18 points) and Roope Hintz (nine assists, 13 points) both have nine-game points streaks. Pavelski has three goals and seven points in his last three games.
Stamkos stopped a 10-game goal drought at 14:32 of the second that tied it at 3. He is one goal away from trying Norm Ullman (490) for 49th place all-time.
Pavelski, on the power play, and Roberston scored 1:55 apart midway through the second to give Dallas a 3-2 lead.
Pavelski moved past Bill Guerin for the eighth-most goals by an U.S.-born player with 430. It was his 156th power-play goal, which tied him for 42nd on the NHL list with Pat LaFontaine.
Paul put the Lightning up 2-1 on the power play early in the second.
Colton opened the scoring 1:20 into the game before Marchment tied it with a power-play goal late in the first.