"I was definitely happy I made it," Smith said. "I wanted to celebrate, but I was too tired."
That's fine, because the Chiefs are suddenly breathing easier after their defense kept Kansas City's perfect start intact.
Smith's interception and linebacker Tamba Hali's 11-yard fumble return for a touchdown aided the Chiefs in overcoming a pedestrian offense and their own leaky defense in securing a 23-13 win over the Buffalo Bills on Sunday.
Kansas City (9-0) remained the NFL's only undefeated team and matched the best start in franchise history set in 2003. The Chiefs now enter their bye week before a key AFC West showdown against the Denver Broncos (7-1) on Nov. 17.
If the only thing perfect about the Chiefs is their record so far, coach Andy Reid refuses to make any apologies.
"We're not going to make excuses for it," said Reid, who in his first year has the Chiefs continuing their worst-to-first run after a 2-14 finish last season. "We're pretty happy that we got the touchdowns. We'll take them any way we can get them."
The Chiefs' defense led the way, outscoring the Alex Smith-led offense, which was limited to three field goals. And the defense had to compensate for its own problems in having difficulty containing a Buffalo offense headed by Jeff Tuel, an undrafted rookie making his first career start.
Despite allowing a season-worst 470 yards of offense and 25 first downs, the Chiefs were opportunistic in holding their ninth consecutive opponent to 17 points or less to match an NFL record set by the 1977 Atlanta Falcons.
Smith's interception turned the momentum, tying the score at 10 after Tuel had marched the Bills 79 yards on the opening drive of the third quarter.
"We don't really care what people think," Hali said of the Chiefs' victories lacking style points. "Sometimes the stats don't really tell you the outcome."
Tell that to the Bills (3-6), who were left stunned and frustrated in attempting to figure out how they let this one slip away.
"Horrible," offensive coordinator Nathaniel Hackett said. "It was shocking even to our guys. We did everything we wanted. We just couldn't finish it."
The difference was turnovers, as the Chiefs turned Buffalo's three giveaways -- two interceptions thrown by Tuel and Graham's fumble -- into 17 points.
The loss marred what began as a solid outing by Tuel, who became the third quarterback to start for Buffalo this season. He played in place of interim starter Thad Lewis, who was sidelined by bruised ribs, and with rookie starter EJ Manuel missing his fourth game with a sprained right knee.
Tuel's 139 yards passing in the first half were the most by a Bills quarterback in the first two quarters this season. And Tuel was in a position to improve his numbers after marching Buffalo to the Kansas City 1 on the opening drive of the second half before his day went awry.
Facing third-and-goal, Tuel took a shotgun snap, and looked immediately to his right, where Graham was running a slant pattern. Tuel, however, failed to account for Smith, who easily picked off the pass at the goal line and then took off up the left sideline.
"It's very frustrating," Tuel said. "That's 100 percent my fault."
Tuel finished 18 of 39 for 229 yards passing, and a 59-yard touchdown to Marquise Goodwin.
For Kansas City, Smith completed 19 of 29 passes for just 124 yards. Running back Jamaal Charles was held under 100 yards from scrimmage for the first time this season.
Kansas City also snapped a six-game losing streak at Orchard Park that included two playoff losses, winning there for the first time since Sept. 28, 1986.