Freeman's inconsistency has been an issue during a slow start by Tampa Bay, however the fourth-year pro is developing a touch on deep passes that's sparked a sputtering offense over the past two games.
He teamed with Mike Williams on a 62-yard scoring play in the first quarter and threw TD passes of 19 and 17 yards to Vincent Jackson in the second half.
Barber, making the transition to safety after 15 seasons as one of the NFL's top cornerbacks, scored his 14th career regular season touchdown when he picked off a pass that bounced off intended target Dexter McCluster and ran up the right sideline to make it 21-3 early in the third quarter.
It was Barber's eighth career interception return for a TD.
Quinn completed 22 of 38 passes for 180 yards, filling in for the injured Matt Cassel, who sat out after leaving the previous week's 9-6 loss to Baltimore with a concussion.
The Chiefs (1-5) scored their only touchdown early in the fourth quarter on Edgar Jones' 11-yard fumble return on a play that began with Shaun Draughn blocking a punt into the end zone.
Bucs punter Michael Koenen chased down the loose ball and ran out to the 1, where he was hit by Draughn as he was trying to throw the ball forward. Jones caught the ball on the fly, but it was ruled a fumble because a pass can't be attempted off a blocked punt.
Williams finished with four receptions for 113 yards, his second consecutive 100-yard game. LeGarette Blount finished the rout with a 12-yard touchdown run.
The Bucs played without cornerback Aqib Talib, who began serving a four-game suspension for violating the NFL's policy on performance-enhancing drugs.
But Quinn couldn't make them pay for not having one of their top defenders.
Tampa Bay limited NFL rusher leader Jamaal Charles to 40 yards on 12 attempts, making the Chiefs one-dimensional on offense.
Rookie Mark Barron had a first-quarter interception that stopped a drive deep in Bucs territory, and Barber's TD capped a three-minute stretch in which the Bucs turned a 7-3 halftime lead into an 18-point advantage.
Quinn, a former first-round draft pick, made his first start since Dec. 12, 2009, when he was with the Cleveland Browns. He didn't get off the bench at all over the past two seasons with the Denver Broncos and played briefly after Cassel was hurt last week.
Freeman was 15 of 26 and was intercepted once by Chiefs linebacker Justin Houston, costing Tampa Bay an opportunity to take an early lead.
The Bucs outgained Kansas City 463 to 260, limiting the Chiefs to 80 yards rushing 141 below their season average of 221.6 per game.
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Kansas City 0 3 0 7 10
Tampa Bay 7 0 14 17 38
TB • Williams 62 pass from Freeman (Barth kick), :18.
KC • FG Succop 38, 7:45.
TB • Jackson 19 pass from Freeman (Barth kick), 12:46.
TB • Barber 78 interception return (Barth kick), 9:36.
KC • Jones 11 fumble return (Succop kick), 14:01.
TB • FG Barth 27, 10:34.
TB • Jackson 17 pass from Freeman (Barth kick), 6:43.
TB • Blount 12 run (Barth kick), 1:53.
Attendance • 46,500.
First downs 15 19
Total Net Yards 260 463
Rushes-yards 30-80 24-145
Passing 180 318
Punt Returns 2-11 3-21
Kickoff Returns 0-0 2-36
Interceptions Ret. 1-32 2-90
Comp-Att-Int 22-38-2 15-26-1
Sacked-Yards Lost 0-0 1-10
Punts 6-46.0 3-35.3
Fumbles-Lost 0-0 2-1
Penalties-yards 7-55 6-33
Time of Possession 33:11 26:49
Rushing • Kansas City, Charles 12-40, Eachus 5-18, Draughn 11-11, Quinn 2-11. Tampa Bay, Martin 13-76, Blount 7-58, Ware 1-6, Freeman 3-5.
Passing • Kansas City, Quinn 22-38-2-180. Tampa Bay, Freeman 15-26-1-328.
Receiving • Kansas City, McCluster 6-39, Maneri 4-45, Bowe 3-21, Draughn 3-12, Baldwin 2-19, Charles 2-7, Eachus 1-19, Moeaki 1-18. Tampa Bay, Williams 4-113, Jackson 4-66, Underwood 2-68, Martin 2-55, Ware 2-10, Lorig 1-16.
Missed Field Goals • Tampa Bay, Barth 55 (WL).