Kansas City, Mo. ? Challenges won and penalties are two stats that all year have been in favor of Kansas City’s rivals.

Collectively, they can add up over the length of a season, and even make the difference between a win and a loss.

In Sunday’s 31-27 victory over Denver, however, they turned around solidly in the Chiefs’ favor. Could a trend be developing just in time for a stretch run to the playoffs?

Probably not, says head coach Dick Vermeil.

“Just luck, I think,” Vermeil said Monday.

The Chiefs had been 0-5 when they threw out the challenge flag. But they finally made a challenge breakthrough against the Broncos.

On one, they nullified a touchdown by Jake Plummer. The Broncos scored two plays later. But on another, the Chiefs gained possession of the ball near midfield when replay officials overruled officials on the field and said the Broncos did not make a first down on fourth and one with 2:01 to play.

The Chiefs then ran the clock down to the three-second mark, sealing a victory that lifted their record to 8-4 and brought them to within one game of the Broncos in the AFC West.

Kansas City defensive end Jared Allen celebrates after the Chiefs defense stopped a Denver scoring drive on downs late in the fourth quarter. The Chiefs beat the Broncos, 31-27, Sunday at Arrowhead Stadium in Kansas City, Mo.

“Sometimes they make a mistake and don’t go along with me,” Vermeil said with a grin.

The Chiefs also came away on the long end of the penalty total. Officials flagged Denver eight times for 55 yards, including several offsides penalties while quarterback Trent Green barked out signals. The Chiefs were penalized six times for 45 yards, with one turning a touchdown pass by Green into a field goal by Lawrence Tynes.

That’s not exactly a wide gulf. But it was an improvement. Going into the game, the Chiefs ranked dead last in the league in penalties against opponents. Chiefs’ opponents had been penalized just 57 times. Denver was No. 2 going the other way, with teams playing against them being called for 104 penalties.

Ironically, the only team whose opponents had been penalized more than Denver was the Dallas Cowboys, who will play host Sunday to the Chiefs.

“That’s the first time we’ve been (outpenalized) in a long time. People love to play Kansas City because they always end up with fewer penalties than us,” Chiefs president and general manager Carl Peterson said.

“I was hoping the pendulum might start swinging the other way.”

Now, the challenge will be to keep up the trend at Dallas.

“What I’m worried about is that we’re going to Dallas,” Vermeil said. “Their opponents get penalized more than anybody in football. Our opponents get penalized less than anybody in football. I don’t know how that happens, but it does happen. We had some things go in our favor yesterday.”

One thing that also went in their favor was the rushing game. Larry Johnson, with his team-record-tying fifth straight 100-yard game, rolled up 140 yards against a Denver defense that was ranked No. 1 against the run, giving up just under 80 yards per game.

“We knew it had to come back to the running, and Larry toughed out yards,” left guard Brian Waters said. “I don’t know what the average was (4.5 yards), but I bet it wasn’t high. We just toughed-out yards. We grinded out every yard. We were determined not to be stopped.”