IRVING, TEXAS ? Dallas Cowboys coach Bill Parcells challenged his struggling offense to “do something” to keep pace with the high-scoring Kansas City Chiefs.

Then, he gave them some gimmicks to help pull it off.

Getting touchdowns on a flea flicker, an end around inside the 10-yard line and a pass to a blocker who hadn’t scored in two years, the Cowboys kept their playoff hopes alive by pulling out a 31-28 victory Sunday in a tense, thrilling game befitting a matchup between Parcells and Dick Vermeil.

Drew Bledsoe had his best game in months, throwing for 332 yards and matching his season-best with three touchdowns. He led Dallas (8-5) on a go-ahead drive early in the fourth quarter, then took the club 68 yards in 14 plays for the winning score – a one-yard pass to tight end Dan Campbell with 22 seconds left.

“That was really a great drive, probably the best one of the year,” Parcells said.

Yet ending their two-game losing streak wasn’t that simple. The Cowboys had to hold their breath as Lawrence Tynes went for a 41-yard field goal that would’ve forced overtime. After a low snap, it went wide right, ending a three-game winning streak for the Chiefs (8-5).

Dallas quarterback Drew Bledsoe (73) and guard Larry Allen (73) celebrate the Cowboys' winning touchdown in the fourth quarter against Kansas City. The Cowboys beat the Chiefs, 31-28, Sunday in Dallas.

The victory for Dallas does more for their confidence and outlook than it does in the standings. The Cowboys could’ve lost this one and still had a chance to finish 10-6, but they would’ve been in a real funk with a three-game losing streak and the next two on the road.

“This is a hugely important game for us,” said Bledsoe, who was 22-of-34 with no turnovers. He also moved into fifth place on the career completions list, 15th on the career TD passes list and matched Warren Moon for the most 3,000-yard seasons. “But we’ve got to keep winning,” he added.

The final play was only part of the frustration for Kansas City. The Chiefs also wasted 143 yards rushing and three touchdowns by Larry Johnson and 340 yards passing by Trent Green, plus a chance to move up in the AFC wild-card chase because of a loss by division rival San Diego.

Kansas City missed a chance to put the game away early as its first five possessions reached at least midfield, but only two ended in touchdowns. The Chiefs were at the Dallas nine, poised to go up 21-10, when Green was sacked by former teammate Scott Fujita and fumbled. Defensive end Marcus Spears returned it 59 yards, leading to a 26-yard touchdown pass from Bledsoe to Jason Witten that put Dallas up, 17-14, at halftime.

Chiefs holder Dustin Colquitt, right, pounds the turf in frustration after kicker Lawrence Tynes (1) missed a 41-yard field goal in the final seconds against Dallas as Cowboys Jacques Reeves, left, and Nathan Jones celebrate. The Cowboys won, 31-28, Sunday in Dallas.

“I’m sick to my stomach,” said Green, who was 20-of-32. “No missed field goal cost us this game. We had many opportunities to win. That’s the disappointing part.”

Johnson ran pretty much at will for three quarters, racking up 126 of his yards by then to set a Chiefs record with six straight 100-yard games. The Cowboys hung in, thanks mostly to Bledsoe and some big plays.

Their first touchdown came on a perfectly executed flea flicker, with the defense falling for the handoff and Terry Glenn speeding past the coverage. Bledsoe heaved it deep, and Glenn caught it in stride for his longest play since December 1998, which also came from Bledsoe during their New England days.

Glenn surprised the defense again early in the fourth quarter by taking a handoff on third-and-one from the six. He wound up with the first rushing touchdown of his career, putting Dallas up, 24-21.

Green regained the lead for Kansas City with a 47-yard touchdown pass to Eddie Kennison with 3:55 left. Then came Bledsoe’s big drive.

He kept it alive with two third-down completions, then Marion Barber III turned a short pass into a 21-yard gain to the six. The Cowboys almost ran out of chances when Witten missed a fourth-down pass in the end zone, but holding was called. Officials pinned it on safety Greg Wesley, but replays showed linebacker Derrick Johnson was to blame.

“I was celebrating, thinking it was over,” Wesley said. “Then I see a flag. I thought, ‘Wow, way to give them a second chance.’ … I made a great play and they were bailed out by the referees.”

Given a second chance, Bledsoe hit Campbell for his third reception of the season and first touchdown since Nov. 9, 2003.

Glenn led Dallas with 138 yards on six catches and Witten had 93 yards on seven grabs. Barber ran for 82 yards.

Kansas City’s Tony Gonzalez caught five passes for 94 yards, and Kennison had 92 yards.

Notes: Parcells now is 1-1 against Vermeil. … The Chiefs fell to 1-4 in games back in the area where they began in 1960 as the Dallas Texans. … Glenn has a career-best seven TDs this season, counting his rushing score. … Kansas City owner Lamar Hunt, a longtime Dallas resident, flipped the coin before kickoff and was honored with a video tribute after the first quarter.