The Chiefs overturned a 17-point deficit and, despite giving up a late touchdown, were able to hold on for their fourth win through five games.
The end result was a far cry from the opening stages of the contest, with quarterback Derek Carr and the Raiders offence rolling downfield on almost every opportunity.
Down 17-0, the Chiefs finally struck blood late in the second quarter when Patrick Mahomes found Kelce in the end zone for his first touchdown.
After both sides exchanged field goals before half-time, Kansas City exploded out of the break with two more touchdowns, while keeping the Raiders scoreless for the entire third quarter.
A field goal to open the fourth brought the Raiders back within one, but the Chiefs were able to hit back with Kelce's fourth score to push the lead back to seven.
A defensive miscommunication then gave up a 48-yard touchdown reception to Davante Adams, but the Raiders were unable to convert the two-point attempt and ultimately ran out of time.