And, both players bounced back in the final minutes to lift Detroit to a 13-10 victory Sunday.
Stafford threw a go-ahead, 31-yard touchdown pass to Kenny Golladay midway through the fourth quarter and Slay made an interception in the end zone with 1:03 left.
"I'm doing this team a disservice if I shut down after two picks," Stafford said.
The Chargers (1-1) were in a position to attempt a 45-yard field goal to tie the game, but Philip Rivers tried to force a pass to Allen and Slay picked it off.
Allen had his way with Slay for much of the day, making eight catches for 98 yards.
"I feel like I was putting on a clinic and then to come down to the last play and he makes a play," Allen said.
The Lions failed to make plays on both sides of the ball in the opener, blowing an 18-point lead in the fourth quarter and settling for a tie at Arizona. Stafford converted a third-down pass to Jesse James with just under a minute left -- a week after a timeout was called just before Stafford completed a pass that could've sealed a win over the Cardinals.
During much of Detroit's home-opening game, though, it looked as though the franchise would have to wait at least another week to earn a win.
Austin Ekeler leaped over the goal line for a 1-yard TD on the Chargers' second drive.
Detroit scored a TD on the ensuing possession with a screen pass that Kerryon Johnson bobbled before securing and sprinting for a 36-yard reception, but Prater muted some of the cheers by missing an extra point to the left. Prater also missed a 40-yard field goal to the right in the second quarter.
The Chargers went from their 3 to the Detroit 21 in 1:16, setting up Ty Long's 39-yard field goal as time expired in the first half to give them a 10-6 lead.
Stafford threw a long pass up for grabs in the end zone early in the third quarter and cornerback Casey Hayward came down with it. Stafford had thrown 181 passes without an interception, which was the NFL's longest active streak.
The Chargers had two TDs negated by flags on the next drive and a penalty by Detroit gave Los Angeles the ball at the 1. Ekeler tried to dive into the end zone again for a score, but rookie Jahlani Tavai forced him to fumble and linebacker Devon Kennard recovered it.
Los Angeles got in position to score again in the third, but Long missed a 39-yard field goal by hitting the left upright. The punter was filling in for kicker Michael Badgley, who missed a second straight game with a groin injury.
Stafford helped the Chargers keep their lead on the next possession, trying to force a deep pass to Marvin Jones and getting it easily picked off by safety Rayshawn Jenkins.
"I felt like that third quarter, it was right there for us to blow the doors off," Rivers said. "And then we kept letting it stay at 10-6."
Los Angeles opted to attempt a 41-yard kick instead of going for it on fourth-and-1 at the Detroit 23 and Long couldn't convert on the field goal early in the fourth quarter.
Detroit coach Matt Patricia chose to pass, instead of kick, on a fourth-and-1 on the ensuing drive and Stafford converted on a pass to Jones to set up his go-ahead throw to Golladay on the next snap.
"That was a laser," Patricia said, reflecting on Stafford's throw to Jones. "I don't know if Marvin caught it or if it just stuck in his chest."
Rivers converted a third-and-10 with a 12-yard run early in the next drive for his longest run since the 2014 season before getting picked off.
HE SAID IT
"There's a lot of bad football in September," Patricia said.
Chargers: Rivers was 21 of 36 for 293 yards and an interception. Ekeler finished with 67 yards receiving and 66 yards rushing for his second straight game with 100-plus yards from scrimmage.
Lions: Stafford was 22 of 30 for 245 yards with two TDs and two interceptions. Golladay had eight receptions for 117 yards. Johnson had 88 yards from scrimmage.
Chargers: Host Houston on Sunday.
Lions: Play at Philadelphia on Sunday.
More AP NFL: https://apnews.com/NFL and https://twitter.com/AP-NFL
'Every detail is first class' -- Tottenham's new stadium passes its first NFL tests in style
The first permanent home for NFL outside the United States arrived a year late, but it was worth the wait.
Which team should be more worried: the Eagles or Cowboys?
Domonique Foxworth and Bill Barnwell disagree about which NFC East contender is in more trouble
Which team is happier with their rookie QB: the Giants or Cardinals?
Domonique Foxworth and Bill Barnwell don't hold back when discussing which top draft pick is playing better so far
Would potential top picks in the NFL draft rather play in Miami or Washington?
Domonique Foxworth and Bill Barnwell debate which struggling team would make for an ideal destination for prospective top picks
Are the Panthers better off with Cam Newton or Kyle Allen down the stretch?
Domonique Foxworth and Bill Barnwell discuss the brewing QB controversy in Carolina
Man mistakenly ID'd, allegedly banned by Browns files lawsuit
Eric Smith has filed a lawsuit against the Browns seeking a public retraction, in addition to financial damages, after he was mistakenly identified as the fan who poured beer on a Titans player.