KANSAS CITY, Mo. — So much for Denver's lucky streak and so long to the longest losing streak in the history of the Kansas City Chiefs.

Larry Johnson ran for 198 yards and two touchdowns and the Chiefs took advantage of four Denver turnovers for a 33-19 victory today over the previously unbeaten Broncos. It was the first win for Kansas City since Oct. 21, 2007, a club-record 12 straight losses that had angry fans calling for the dismissal of everyone from the general manager to the quarterbacks coach.

Nick Novak kicked three field goals for the Chiefs (1-3), who did not seem to be out of danger until Tony Gonzalez snared a 10-yard touchdown pass that made it 23-13 with 12:40 to go.

But with 2:09 left, Denver's Matt Prater kicked a 33-yarder that brought the Broncos (3-1) to 26-19. But following Dantrell Savage's 51-yard kickoff return, Johnson broke two tackles on a 16-yard scoring run to salt away what Herm Edwards, the coach of the win-starved Chiefs, had said would feel like "three Christmases rolled into one."

The Broncos came to town one of five 3-0 teams, thanks in no small part to a series of lucky breaks that included an official's premature whistle and New Orleans' kicker Martin Gramatica's sudden, unexpected inaccuracy.

In the early going, their luck seemed to hold as the Chiefs, with an offense averaging fewer than 11 points a game, turned early touchdown opportunities into short field goals.

But Denver quarterback Jay Cutler kept misfiring and Johnson kept running, and the Chiefs, 10-point underdogs at home, finally broke their skid.

The Broncos tried an onside kick after Prater's 33-yard field goal made it 26-19 with 2:09 left. A Denver player got his hand on the ball. But Kansas City's Kolby Smith emerged from a big pile holding the ball and Johnson quickly scored the clinching TD.

In its first two possessions, Denver's league-leading offense had a turnover, a sack and a shanked punt.

But the Chiefs failed miserably to capitalize. After Johnson got things going with a career-long 65-yard run to the 21 on the game's second play, KC had first-and-goal from the 9. But they came away with only a 23-yard field goal, giving the Chiefs their first lead since halftime of their game against Tennessee last Dec. 16 — a span of 22 quarters.

A big hit by Turk McBride caused Eddie Royal to fumble on Denver's first possession, and Brandon Carr scooped up the ball. The Chiefs moved to a first down on the Denver 12, but Novak came in on fourth down to kick a 21-yarder as the crowd booed.

Brett Kern's 26-yard punt a few minutes later gave the Chiefs the ball on their own 48. But Novak missed from 48 yards.

Cutler was 29-for-49 for 361 yards and two picks. He connected with Brandon Marshall on a 16-yard TD pass that gave the Broncos a 7-6 lead until Johnson scored on a 1-yard run after cornerback Brandon Flowers returned Royal's fumble 37 yards to the 2.

Gonzalez, the 12-year veteran who holds NFL records for tight ends for touchdowns and completions, came within 3 yards of breaking the tight end yardage record. He lay on the end zone several minutes after his TD catch and the crowd chanted, "Ton-Y! Ton-Y!"