Howden tied the game 1-1 at 8:09 after he took the puck in from the right wing and went around Nedeljkovic's right pad as he cut across the net mouth.
"I thought we did a good job of trying to stick with it. Some nights, pucks aren't going your way," Howden said. "We got a fortunate bounce there at the end."
Wennberg put the Sharks ahead 2-1 with a 5-on-3 power play goal at 6:59 of the second period. William Eklund's one-timer from the right circle rebounded off Vegas defenseman Brayden McNabb to Wennberg in front for an open tap-in.
Dorofeyev made it 2-2 with a power-play goal at 14:22. Eichel fed a pass from the left wing to Stone at the goal line. He then slid a pass across the crease to Dorofeyev at the right circle for a one-timer.
Kurashev gave San Jose a 3-2 lead with a goal at 2:59 of the third period when he deflected Dmitry Orlov's slap shot from just outside the top of the left circle.
Eichel tied the game 3-3 while Vegas had an empty net at 18:26 on a dump-in from center ice. Eichel lifted the puck into the Sharks zone, where it landed and then bounced awkwardly by Nedeljkovic.
"Just got caught in between on the third one, whether to go out and try to catch it in the air or let it bounce and hop," Nedeljkovic said. "Usually when you're in between at this level, bad things happen."