Alex Smith scored on a 1-yard touchdown run with 9:20 remaining in the third quarter to give the Chiefs their first lead, 14-10. Kansas City, which trailed 10-0 in the first quarter, took the second-half kickoff and went 79 yards in 10 plays.
The Chiefs were aided by two defensive penalties on Washington.
But Washington answered right back less than two minutes later as Ryan Grant scored on a 3-yard pass from Kirk Cousins. The touchdown was set up by a 69-yard catch-and-run by tight end Vernon Davis to the Kansas City 6.
Grant’s score with 7:42 remaining has Washington back in the lead, 17-14.