Smith was solid in regulation, especially in the third period, when the Sharks outshot the Coyotes 15-3.
It was the second shutout of the season and 21st career whitewash for Smith.
Niemi, meanwhile, recorded his first shutout of the season and the 20th of his career, stopping all 21 shots he saw in regulation and the overtime.
The loss was the fourth straight for the Sharks.
Wisconsin business offering 'therapeutic cuddling' forced to close
Megyn Kelly: Santa Claus and Jesus are both white men