It took him less than five minutes to throw two touchdown passes, or one more than he'd thrown in the last two games combined.
After Tyreek Hill's 40-yard catch put the ball at the Jets 23, Smith completed a 4-yard pass to Travis Kelce, who had two early touchdowns.
To start with the good, quarterback Alex Smith played his best game since the teams' last-second loss to the Oakland Raiders six weeks ago.
Still it wasn't enough.
Josh McCown scored the game-winning touchdown, a one-yard rush, with 2:20 left to play to lift NY (5-7) to its first victory since November 2 against the Buffalo Bills.
The Jets (5-7) blew fourth-quarter leads in three of their previous five games heading into this weekend. After McCown's go-ahead touchdown, the Chiefs drove down to the Jets' 19-yard line.
It was announced earlier in the day that Chiefs head coach Andy Reid ceded play-calling duties to offensive coordinator Matt Nagy, and the move seemed to pay immediate dividends in a high-scoring first quarter.
The Chiefs were flagged for defensive holding again on the ensuing two-point conversion attempt. That didn't appear to make much of a difference. Third-down defense was as brutal as watching new Chiefs cornerback Darrelle Revis look like a shell of his former self in one half of action before being mercifully benched in his Kansas City debut.
Both the Jets and Chiefs have lost five of six and are trying to get their seasons back on track. The Chiefs generally script those plays well before kickoff; they are not selected in the moment.