KANSAS CITY, Mo. -- Alex Smith scrapped himself off the Arrowhead Stadium turf and he wanted to let all the emotion of a crazy afternoon of season opening football flow. But, the Kansas City Chiefs quarterback knew he had to wait.

Smith had just scored on a 2-yard run a little over five minutes into overtime to give the Chiefs a come-from-behind 33-27 victory over the San Diego Chargers on Sunday. Down by 18 points in the first half and 21 in the second half, Smith and his teammates mounted the biggest comeback in franchise history with 23 unanswered points.

Smith's touchdown was under replay review, and over 12 NFL seasons he has seen a lot of crazy things happen. Eventually referee Jerome Boger said those magic words "the play stands" and the Chiefs walked away with a victory unlike any in the club's 56 years of football.

"I heard him say they were going to a review and sometimes on those goal line plays you have no idea what might show up," Smith said. "A knee may hit a fraction earlier, and where's the ball? Everybody was going nuts, but I didn't want to start celebrating.

"When he finally said it was a touchdown, I lost it. With the comeback and that play on third down, there were a lot of emotions."

Kansas City trailed 21-3 at halftime and then 24-3 after six minutes of the third quarter. But the Chiefs scored three touchdowns and a field goal in the second half. They won the overtime coin toss and drove 70 yards on 10 plays before Smith ran right, dropped his head and blasted into the end zone.

"In the first half, all three phases were brutal," head coach Andy Reid said of his offense, defense and special teams. "In the second half, we settled down and played like we normally play. A lot of good things happened."

A fourth-quarter decision by San Diego head coach Mike McCoy helped spark the Kansas City comeback. With 11 minutes, 25 seconds to play, the Chargers had the ball at the Chiefs 36-yard line.

They faced a fourth-and-2 while holding a 27-10 lead. Deciding against a punt that would have pinned the Chiefs deep in their own territory, McCoy tried a 54-yard field goal. Josh Lambo's kick sailed wide right and Kansas City took over at its own 44-yard line.

Seven plays later, Smith connected with wide receiver Jeremy Maclin for a 19-yard touchdown pass that cut San Diego's lead to 10 points. A 33-yard field goal by Cairo Santos chopped the margin to seven and Kansas City tied it up with 63 seconds to play on a 5-yard touchdown scamper by running back Spencer Ware.

"I thought he was going to make it," McCoy said of the 54-yard field goal try. "I had all the confidence in the world in him (Lambo). It gave them good field position and we still have to stop them. We had been doing a very good job all game long, but we didn't do a good job after that. That was the turning point."

Smith was 34 of 48 for 363 yards and two touchdown passes and had 15 rushing yards. Ware, starting in place of the inactive Jamaal Charles, produced 199 yards from scrimmage.

It was a remarkable turnaround for the Chiefs. Chargers quarterback Philip Rivers sliced and diced the Chiefs' defense, producing touchdowns on three of four possessions over the first 30 minutes. Running back Melvin Gordon scored on runs of 1 and 6 yards, and Rivers found running back Danny Woodhead wide open in the end zone for the third touchdown on a 4-yard pass play.

"It was a game where for three quarters and change, we had control," Rivers said. "You've got to give them credit, they had an awesome fourth quarter and we didn't do anything to counter."

Until that fourth quarter, he Chargers defense tormented the Chiefs offense. Only Ware was able to consistently generate offense. It was his 45-yard catch and run late in the third quarter that set up Kansas City's first touchdown. Smith connected with wide receiver Tyreek Hill on a 9-yard scoring play that began the Chiefs second-half comeback.

"I think every guy in there knows how bad we played, how poorly we played," Smith said. "Some things went our way in the second half and we were able to get out of here with a W. As great as it is to win, there's going to be a lot to improve on."

NOTES: The Chargers also suffered a stunning loss when WR Keenan Allen went down near the end of the first half with a probable torn ACL in his right knee. Allen was removed from the field on a cart and did not return to the game. ... San Diego's first-round draft choice DE Joey Bosa did not dress for the game due to a hamstring strain. Bosa missed all of the preseason in a contract dispute and continues to carry a roster exemption from the NFL. ... The Chiefs lost backup LB Sam Barrington in the second half with a hamstring injury. ... Chiefs RB Jamaal Charles was inactive. He is recovering from a torn ACL and last played in October 2015.