Needing only to eke out a win, the Buffalo Bills wound up smashing a record. A mistake-free Trent Edwards threw for two touchdowns and ran for two more and the Bills romped past Kansas City 54-31 Sunday, breaking a four-game losing streak while scoring more points than anyone ever scored before against the Chiefs. Snapping smartly out of a demoralizing slump that threatened to waste a 5-1 start, the Bills came within four points of matching their 42-year-old record for points in a game. The Chiefs (1-10) had five turnovers while losing for the 19th time in 20 games, by far the worst stretch in franchise history. "Its embarrassing," said Chiefs linebacker Derrick Johnson. The Bills (6-5) scored 20 points off turnovers. "They worked hard, obviously, preparing for this game, and they got a lot of bounces," Bills coach Dick Jauron said. "They made a lot of plays." Edwards became the first Bills quarterback since Jack Kemp to run for two TDs in a game. He looked nothing at all like the guy who in his 13 previous quarters had thrown eight interceptions while losing two fumbles and managing only three touchdown passes. "I always try to be confident," said Edwards. "Even when Im not, I try to act like I am. Thats the position you have to be in." Edwards hit 24 of 32 for 273 yards and two TDs and had touchdown runs of 5 and 15 yards. "Our defense was forcing some turnovers for us," he said. "We were getting good field position with special teams and as a result of turnovers." The previous high against the Chiefs was 51 in an overtime loss at Seattle in 1983. The Chiefs, who had thought they were starting to turn the corner after playing their last four opponents close, were also penalized nine times for 75 yards. "I anticipate theyll come to work Monday," coach Herm Edwards said. "They know what they did wrong. Youve got to play smart and not turn the ball over and be careful with the fouls." Rian Lindell kicked four field goals and Leodis McKelvin, the Bills rookie first-round choice making his second start at cornerback, had two interceptions and returned two kickoffs a total of 67 yards. He returned his first interception 64 yards for a touchdown and his second led to Edwards 15-yard touchdown run at the end of the half. `It was just me getting the opportunity to play," said McKelvin, the 11th overall pick in last years draft who started in place of injured Jabari Greer. "I was just behind two guys playing great at the start of the season. I was just sitting back. I knew my time would come," he said. "I had two guys in front of me who had been in the league for five and six years, so they knew how to play." The Bills scored 20 of their record-setting points off turnovers, including two field goals, one of Edwards scoring runs and McKelvins TD return. Tyler Thigpen, the former third-teamer who was pressed into service after injuries put Kansas Citys top two quarterbacks out for the year, had his first bad game in five outings. Besides the two picks to McKelvin, he also lost one of the fumbles. But he also hit 17 of 31 passes for 240 yards and three touchdowns. "Thats one thing I cant do. I cant turn the ball over, and thats something I did three times today," said Thigpen, who had gone 161 straight throws before getting one picked off last week. "I cant do that, bottom line." When Derek Schouman caught a 17-yard pass for Buffalos final TD, normally volatile and demonstrative defensive coordinator Gunther Cunningham stood stock-still for perhaps 20 seconds, staring into space. "It felt like a loss by 30 points, no different," said safety Jarrad Page. "You lose by 30 points, its bad - 54 or whatever. A 30-point loss is big." Edwards also connected with Josh Reed on an 8-yard TD pass. The most embarrassing TD for the Chiefs was the 15-yard Edwards run at the end of the first half. The Bills were out of time outs with 26 seconds left when Tamba Hali flushed him out of the pocket. All the Chiefs had to do was tackle him, and Buffalo could not have stopped the clock for a fourth-down play. But the second-year pro scrambled away and dived across the line for a 15-yard TD run and a 30-17 halftime lead. Notes -Before Sunday, Edwards had only one touchdown rushing. -The Chiefs actually outgained the Bills 462-444. -Chiefs TE Tony Gonzalez had 10 catches for 113 yards and set a tight end record with his 25th 100-yard receiving game. -In their previous four games, the Buffalo offense had scored only five touchdowns.