The No. 1 overall draft pick from the 2009 NFL draft had three interceptions before halftime for the first time.
Stafford led an 80-yard, nine-play, game-winning drive that included three passes of at least 18 yards and was capped by enough patience in the pocket to connect with a wide-open Smith.
"Kevin was the last option on that play, probably behind throw it away because he was part of the play action and protection," Detroit coach Jim Schwartz said. "The head coach was on the headphones, 'Throw it away Matt, throw it away!' It shows you what a good quarterback I'd be."
Stafford finished 32 of 48 for 355 yards.
"I knew in that formation Calvin would get all of the attention," Stafford said. "That's exactly what happened."
St. Louis coach Jeff Fisher, who is leading a franchise coming off the worst five-year span since the 1970 NFL-AFL merger, put together a conservative game plan that almost worked.
"Our plan was to try to hold them to field goals ... and then take your shots offensively," Fisher said. "Get your points and have a chance to win the game at the end."
Bradford was hit by defensive end Cliff Avril on the game's last play, leading to some pushing, shoving and shouting that didn't get out of hand in part because the officials separated the players. The replacement officials included line judge Shannon Eastin, who became the first woman to officiate an NFL regular-season game.
Steven Jackson gained just 53 yards on 21 carries for an offense that couldn't take enough time off the clock on its next-to-last drive to prevent Stafford from getting the ball back.
"Give the Lions credit, they made the big plays they needed at the end of the game," Finnegan said. "We did some really good things, but we've got to learn how to finish. That will come."
Fisher said Saffold was alert and had strength in his arms and legs.
"This is more of a precautionary deal," Fisher said. "There's a chance he'll come home with us."
"We gave ourselves a chance to stay in the game and win it at the end," Fisher said. "I think we got better as a team."
Early on, it looked like Stafford had taken a step back after throwing for 5,000-plus yards, 41 touchdowns and 16 interceptions last season to help Detroit end an 11-year postseason drought.
"We did a ton of film study on Stafford, and we knew what he likes to do," Finnegan said. "Our coaches gave us a great game plan ... We just needed to make one more play."
Stafford, though, was the one who came up with the clutch plays to avoid an upset in the opener for both teams.
"It wasn't like he was just having a bad day," Schwartz said. "He had a couple of bad plays.
"You have to have a demeanor that allows you to come back from that."
NOTES: Replacement official Paul Caldera left the game in the third quarter with an apparent leg injury. He was replaced by alternate Curtis - a replacement for the replacement. ... Detroit wide receiver Titus Young was called for unnecessary roughness after he head-butted Jenkins. "It was right in front of me the whole time," Schwartz said. "It looked like he was going to walk away and do the right thing and then he made a dumb decision." ... Fisher hired Schwartz in 1999 to be on his staff at Tennessee and promoted him two years later to the Titans' defensive coordinator, a job he had until Detroit gave him his first shot to be a head coach three years ago. ... Lions rookie CB Bill Bentley left the game with a concussion. ... St. Louis wide receiver Danny Amendola had five catches for 70 yards.