Victor Munoz saved Andoni Iraola from his first defeat as Liverpool manager with the late strike that rescued a 2-2 draw against Nottingham Forest on Saturday, while Newcastle condemned big-spending Tottenham to a second successive defeat.
Forest were set to win at Anfield for the third consecutive season as Dan Ndoye and Morgan Gibbs-White's penalty twice put the visitors in front.
Alexander Isak briefly brought Liverpool level in the second half before Munoz's deflected effort rescued a late point for the second time in Iraola's two matches in charge.
"It's quite clear the first half has been poor, we haven't controlled the game," Iraola said.
"We improved a lot in the second half, much more intense, much quicker on the ball but not enough to win the game."
After a 2-2 draw at Newcastle in his first game as Liverpool boss last weekend, Iraola had hoped for a memorable day to mark his first match in charge at Anfield.
But instead the former Bournemouth boss got a reminder of why he was hired to replace the sacked Arne Slot in the close-season.
Iraola could have Bradley Barcola to unleash by the time Liverpool are next in action at Ipswich on Friday.
The France winger has been one of the Reds's top targets for months and a £106 million ($144 million) deal with Paris Saint-Germain, which could rise by a further £17 million, is reportedly close to completion.
At the Tottenham Hotspur Stadium, Roberto De Zerbi's men endured a dispiriting 2-0 defeat.
Anthony Elanga put Newcastle ahead in the 62nd minute before Yoane Wissa killed off lacklustre Tottenham 10 minutes later as their frustrated fans streamed to the exits long before the final whistle.
Newcastle manager Matthias Jaissle was able to celebrate his maiden Premier League win after a 2-2 draw against Liverpool in the German's first game following his surprise appointment as Eddie Howe's replacement.
It was another chastening result for De Zerbi, whose expensively assembled team suffered an embarrassing 3-0 defeat at Brentford in the opening game of the season last weekend.
HULL ON THE RISE
Tottenham have spent over £300 million ($406 million) in the close-season as De Zerbi overhauled a squad that narrowly avoided relegation on the final day of last term.
But for the first time since 1992-93, Tottenham have failed to score in their first two games of a league season.
Omar Marmoush, Tottenham's latest new recruit, failed to impress on his debut after joining on loan from Manchester City this week.
"There is no panic. I know where we are going and what the plan is. I'm sorry for the fans for the result," De Zerbi said.
"We have to improve. We have to work hard on the pitch and find the connection between the players."
Elsewhere, Hull substitute Liam Millar struck in the closing stages to steal a 1-0 win at Coventry as the Tigers extended their dream return to the top-flight.
Millar slotted home with eight minutes left as Hull won a battle between sides promoted from the Championship last term.
Having stunned Manchester United with a 2-0 victory last weekend, Sergej Jakirovic's men have won both their matches in their first season in the top tier since 2016-17.
Frank Lampard's Coventry won the Championship to end a 25-year exile from the Premier League, but they are still awaiting their first point back in the big time after losing their opener at Arsenal last week.
James Tarkowski's stoppage-time equaliser earned Everton a 1-1 draw that left Marco Rose still waiting for his first win as Bournemouth manager.
Alex Scott's 41st-minute goal put Bournemouth ahead at the Vitality Stadium.
But Everton defender Tarkowski capitalised on a mix-up between Ryan Christie and Marcus Tavernier to drill home following a corner in the closing seconds.
Everton remain unbeaten after a 2-0 win against Crystal Palace last weekend, while Bournemouth lost 2-1 at Manchester City in Rose's first game since replacing Iraola.