The struggling Jets were then on the wrong end of a fortuitous second touchdown for the Chiefs as Calvin Pace tipped Smith's pass straight into the lap of Anthony Fasano, who reached into the endzone for an unorthodox two-yard score.
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Kansas City were soon 14 points ahead once again, however, as Smith picked out Travis Kelce for a 12-yard score with less than a minute remaining in the first half.
Cody Parker kicked a field goal for the visitors as time expired in the second quarter to chip away at the Chiefs' lead, but Cairo Santos made one of his own in the third to keep his side comfortably ahead.
That was how it stayed following a scoreless final quarter as the Chiefs moved to 5-3 to the season, while the Jets slump to 1-8.