KANSAS CITY, Mo. -- Jameis Winston turned in one of the best days of his young career on Sunday against the Kansas City Chiefs, leading the Tampa Bay Buccaneers to a 19-17 upset win on the road.

It was a winning performance that began Wednesday when the second-year quarterback distributed a letter to his teammates. The tone of the missive was how proud he was to be quarterback of the Buccaneers. After practice last week, he read the letter in a team meeting.

"It's team stuff; Iā€™m not going to talk about it," Winston said. "One thing I can say, I told them how grateful I was to be their quarterback."

At Arrowhead Stadium on Sunday, everybody with the Buccaneers (5-5) was grateful that Winston was their offensive leader.

Winston threw for 331 yards, and his 3-yard touchdown pass to tight end Alan Cross midway through the fourth quarter gave the Buccaneers a lead that Kansas City could not overcome. It was a second consecutive victory for Tampa Bay, which is 5-1 on the road this season.

The outcome ended a five-game winning streak for the Chiefs (7-3) and stopped a 10-game stretch of victories for the home team at Arrowhead Stadium.

"Jameis was out of sight today," Buccaneers coach Dirk Koetter said. "That's as good a quarterback play as I've seen in however many years I've been in the league. He was awesome. Jameis played a great, great game. We gave him the game ball already."

The Kansas City defense limped into the game, opening without starters Jaye Howard at left defensive end and Marcus Peters at left cornerback. Both players were out with hip injuries.

Then outside linebacker Dee Ford, among the league's top pass rushers with 10 sacks, went down in the first half with a hamstring injury.

Kansas City could not get Winston and the Tampa Bay offense off the field. Although the Buccaneers scored only the one touchdown, they racked up 442 yards on 74 plays and finished with a 10-minute, 36-second edge in time of possession.

"We couldn't get them off the field defensively and we couldn't stay on the field offensively," Chiefs coach Andy Reid said.

Winston completed 61.5 percent of his throws and averaged 8.5 yards per attempt. Wide receiver Mike Evans, ranked among the league leaders coming into the game, finished with six catches for 105 yards.

Kansas City quarterback Alex Smith scored on an 11-yard touchdown run in the first half and connected with wide receiver Albert Wilson on a 2-yard scoring pass late in the game.

But another opportunity for the Chiefs was snuffed when Smith's pass into the end zone was picked off by Buccaneers safety Chris Conte and he brought it out 55 yards. That return set up the Tampa Bay offense at their 48-yard line.

"No. 23 was supposed to bite on that (play-action) fake," Reid said of Conte. "He has been biting on that. Today, he didn't bite on it."

Nine plays later, Winston connected with Pace on a third-down pass from the Kansas City 3 and provided Tampa Bay with a nine-point lead.

"I can't tell you how major a play that was," Buccaneers safety Bradley McDougald said of the interception. "Late in the game, their offense is driving and they're gaining momentum play by play. Not only does he come down with it, he returns it to midfield and gives our offense good field position. It's the play of the game."

Kansas City came back and put together a 12-play, 78-yard possession that saw Smith and Wilson find the end zone on third down with 2:27 on the game clock. The Bucs made sure there was little time left for the Chiefs to attempt a potential winning field goal.

Winston did not want to talk about the victory being a statement game for the young Buccaneers. But he acknowledged it was a major step forward for the team.

"I think that set the standard for our organization," Winston said. "We were talking in the shower about how it felt great, and Gerald McCoy said 'that's expected.' I paused for a moment and told him, 'you're exactly right.'"

The Buccaneers will find out quickly how far forward they've come, as they host Seattle next Sunday. The Chiefs will go on the road to face a Denver Broncos team coming off its bye week with a 7-3 record.

NOTES: The kickers were busy. Tampa Bay's Roberto Aguayo hit all four of his field goal attempts (31, 22, 41 and 36 yards) and Kansas City's Cairo Santos was good from 22 yards. ... The Buccaneers have now won five straight against the Chiefs and have not lost to Kansas City since September 1983. Based on the NFL's scheduling formula, the teams won't see each other again until the 2020 season. ... Tampa Bay CB Brent Grimes left the field in the first quarter with a quadriceps injury. He did not return.