Brady passed for 340 yards and a touchdown and ran for another score, diving head-first between two defenders in a rare run by the 41-year-old quarterback.
Thanks to Hill, it took them only one play to do exactly that.
The Chiefs (5-1) rallied from a 15-point halftime deficit to go up 33-30 with 8:38 remaining.
Another reason would be looking at the injuries on the Chiefs side.
The Titans, however, have now suffered back-to-back defeats since beating Super Bowl champions Philadelphia Eagles as they slumped to a 21-0 shutout loss to the Baltimore Ravens in Nashville. He makes pretty much every play the Chiefs run look like it was drawn up on the spot by some open-minded offensive genius. "We can take this loss".
The journey to 43-40 was as entertaining and jammed with intrigue as any other regular-season game in recent memory.
Sunday night's battle against a new AFC challenger was no different from those hyped contests of the past. "We're going to go out there, and hopefully we can keep playing, and hopefully we might be able to see him again". Had Gostkowski missed, it would have forced New England into having to score a touchdown to win the game and it can't be understated how important that field goal was.
Tom Brady has set plenty of records in his illustrious career. The fan who threw beer on him after touchdown No. 3 will certainly regret his decision for a long time.
When asked about the decision to entrust Gostkowski with a 50-yard kick as the game hung in the balance, coach Bill Belichick astutely observed that his kicker's contributions are often overlooked - inadvertently remind us that he was actually the hero of the game. Tailback Kareem Hunt also had a big night in the passing game for Kansas City, hauling in five catches for 105 yards - including a 67-yard pass that ignited the Chiefs' rally in the third quarter. This has to improve if they're going to get where they want to go, but it remains to be seen how they will go about it.
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