Arsenal lost 1-0 at Newcastle United, meaning Mikel Arteta’s side have managed only one point from their last three games.
Nottingham Forest’s dream start to the season continued as they crushed West Ham United 3-0 to move into third place.
Liverpool have 25 points from 10 games with City on 23 while Forest have 19. Arsenal are fourth with 18 points although could slip out of the top four if fifth-placed Aston Villa avoid defeat at Tottenham Hotspur on Sunday.
Slot has enjoyed the best start by any new Liverpool manager since replacing Juergen Klopp and Saturday’s victory was his side’s 13th in 15 matches in all competitions.
While the defeats for City and Arsenal were a bonus, the Dutchman said he was only concerned with his own side.
“Not because of those results but it feels special because we faced Arsenal last week who are a very tough team,” he said.
“Today we faced the same quality and idea about football and both times we had to come from behind to get a result. That is what makes my day, not so much the results from other games.”
Liverpool fell behind after 14 minutes against Brighton with Turkey international Ferdi Kadioglu rifling in a stunning effort as the visitors seized control.
Slot’s side were struggling to get back on level terms but got a break when Cody Gakpo’s 69th-minute cross went straight into the net to lift the mood.
Three minutes later Salah curled home a stunning effort from the right side of the penalty area and that proved enough.
“The second goal was a Mo Salah special,” Slot said.
City boss Pep Guardiola had lamented his side’s injury list in the build-up to their game at Bournemouth and his side were without John Stones and Ruben Dias as well as several others as their club record 32-game unbeaten Premier League run ended.
“We couldn’t match up to the intensity,” Guardiola said.
MISERABLE RUN
Bournemouth had lost all 14 of their previous Premier League meetings with City with an aggregate score of 45-7 but ended that miserable run as City lost for the second time this week after a League Cup exit at Tottenham Hotspur on Wednesday.
Bournemouth went in front after nine minutes with Antoine Semenyo touching in a low cross by Milos Kerkez.
Evanilson doubled the home side’s lead in the 64th minute after more good work by Kerkez before Josko Gvardiol halved the deficit to set up a tense finale in which Erling Haaland somehow hit the post from point-blank range.
Arsenal managed only one shot on target in the early kickoff at St James’ Park where Newcastle striker Alexander Isak’s early headed goal proved the difference between the sides.
Forest won a third Premier League game in a row for the first time since 1999 as they took West Ham apart.
In-form striker Chris Wood gave his side the lead against West Ham who were reduced to 10 men on the cusp of halftime as Edson Alvarez chopped down Anthony Elanga. Callum Hudson-Odoi doubled Forest’s lead after the break before Ola Aina blasted in a third goal to send the City Ground fans into raptures.
“I think we can get better,” Forest manager Nuno Espirito Santo said of taking Forest as high as third in the Premier League for the first time since 1998, said.
Promoted Southampton celebrated a first Premier League victory of the season as Adam Armstrong struck a late winner to clinch a 1-0 triumph over Everton at St Mary’s.
Ipswich Town thought they hade also registered a first Premier League win of the season as they led Leicester City 1-0 at Portman Road thanks to a Leif Davis volley.
But Jordan Ayew scored deep into stoppage time to salvage a point for Leicester. Ipswich had tried to hang on with 10 men after Kalvin Phillips was sent off with 12 minutes left.
Ipswich and Southampton both remain in the relegation zone with Wolverhampton Wanderers still bottom after a 2-2 draw at home to Crystal Palace in the late kickoff.
