Officers say they tried to make contact with Race on Friday after receiving a tip, but when they approached, he was armed with a knife.
In a release, police say officers fired "less-lethal" beanbag rounds, but they were unsuccessful in stopping Race. Race was armed with a knife and continued to advance towards police, forcing one of the officers to fire his gun.
Race died on scene, police say.
Mesa police say DNA testing confirmed a match between Race and blood evidence collected at the nail salon homicide scene. Police executed a search warrant and found several knives among other evidence. Further testing will be done to determine if any of those knives were used in the homicide.
Lindsey Eastridge's family came to the scene Friday afternoon.
"Today I think is going to help a little bit," said Eastridge's sister, Carla Webber. "This past month has been terrible, it's been absolutely awful."
Only a few hundred yards separate the locations of Friday's officer-involved shooting and Eastridge's murder last month.
"She's absolutely incredible and this shouldn't happen to anybody," Webber said.