The Kings and Cavaliers kept the score close throughout the first half while DeMarcus Cousins nearly had a double-double at the end of the second quarter with 11 points and nine rebounds.
The Kings were able to separate themselves from the Cavaliers, going up by 10 points near the end of the third quarter.
Kyrie Irving caught fire for Cleveland to give his team a 90-89 lead, but John Salmons and Aaron Brooks delivered big shots in the clutch.
After Brooks missed the second of two free throws, Irving launched a halfcourt shot at the buzzer. His shot bounced off the rim and the Kings escaped with a 97-94 win, their second road win of the season.
Cousins was dominant with 18 points, 16 rebounds and six assists for the Kings and Jason Thompson added 19 points and 10 rebounds.
Francisco Garcia had 14 points and six rebounds and Brooks had 13 points off the bench.
Irving finished with 22 points, five rebounds and six assists for the Cavaliers, Alonzo Gee had 16 points and 10 rebounds and six assists and Dion Waiters scored 20 points off the bench.
After playing the second of back-to-back games, Kings coach Keith Smart thinks his team played well and needs everyone to contribute:
"We have to because (we) don't have that deliberate, 100 percent, every night guy. So, we have to have everyone being productive at all times on the basketball floor and when we don't have that we're going to struggle."
The Kings will travel up north to play the Toronto Raptors on Friday at 4 p.m. PST. Evans will rejoin the team in Toronto.