Stone gave the Golden Knights a 2-1 lead at 3:27 of the second period with a backhand shot around Georgiev's pads at the top of the crease.
Smith tied the game 2-2 for the Sharks at 5:53 after Macklin Celebrini collected his own rebound and slid a pass to his right for a tap-in goal.
"I think I definitely was due," Smith said. "I mean, obviously, you want to score all your chances, but it's just not going to happen. You just have to stick with it."
Tyler Toffoli gave the Sharks a 3-2 lead at 15:57 with a shot that deflected off Nicolas Hague's leg from behind the net.
Brayden McNabb tied the game 3-3 for the Golden Knights with a short-handed goal at 1:03 of the third period. McNabb took the puck in on the left wing, scored with a toe-drag shot around Timothy Liljegren, and beat Georgiev on the glove side.
"That was a big goal, great goal," Alex Pietrangelo said. "McNabb's skill is so underrated."
Eichel scored 23 seconds later to give the Golden Knights a 4-3 lead with another short-handed goal. The center split the defense before going to his forehand and around Gerogiev for the goal.
"We knew we had to come back to our game," Golden Knights forward Tomas Hertl said. "It was a nice win after the Christmas break, but we have to be ready against anybody."