Wilfried Zaha had appeared in each of Crystal Palace's last 59 games in the English Premier League stretching back to February 2019.
Conor Coady hadn't missed a minute of Wolverhampton's 84 league games since its promotion back to the top division in 2018.
The two mainstays were unavailable while they isolated during the coronavirus pandemic and that took its toll on their teams on Monday.
Palace was toothless in attack without Zaha, who tested positive for COVID-19 ahead of the game, and slumped to a 1-0 loss to a Burnley side that hadn't previously won in the league. Chris Wood scored in the eighth minute.
Coady was missing for Wolves, having had to train in isolation after discovering he inadvertently came into contact with somebody who tested positive for the virus. With fellow center back Romain Saiss also out after contracting the virus, Wolves switched to a four-man defense for the first time since May 2017 — before the arrival of current coach Nuno Espirito Santo — and was uncomfortable until a late rally earned a 1-1 draw at home to Southampton.
Southampton led through a tap-in from Theo Walcott, who scored his first goal since returning for a second spell at the south-coast club where he started his professional career.
Pedro Neto came off the bench to rescue a point for Wolves in the 75th.
That equalizer stopped Southampton climbing to third place after nine games. Wolves and Palace are in midtable, while Burnley's first win of the season lifted Sean Dyche's team out of the bottom three.
Walcott's goal means he he has scored at least once in 14 straight Premier Leagues.
“I’m only 31 but I feel like a kid again,” said the forward, whose career has been rejuvenated since he moved back to Southampton in a loan switch from Everton, where he was out of the picture. "I’m fit, I love the Premier League.”
The former England winger missed a one-on-one chance at 1-0, shooting wide of the post when clean through, and that cost Southampton when Raul Jimenez's effort came back off the post to allow Neto to sweep home the rebound.
“For everyone, it was a tough game, tactically so demanding,” Southampton manager Ralph Hasenhuttl said. “It was like chess. They played 4-3-3, we didn’t expect that, but we found the answers.”
Burnley manager Sean Dyche acknowledged he felt nervous in the final minutes as his team saw out the win against Palace to finally launch its season.
“It gets a bit nervy because we hadn’t found that first win,” Dyche said, “so to get that one done will do us the world of good.”
It needed a superb sprawling save from Burnley goalkeeper Nick Pope off substitute Christian Benteke in stoppage time to preserve the lead.
Wood's goal came when he latched onto a neat flick by strike partner Jay Rodriguez and sidefooted powerfully past goalkeeper Vicente Guaita from a central position.
Palace has lost 20 of its 28 Premier League games without Zaha since he returned to the club in 2014-15.