The Blues found themselves a man down at the break after Andreas Christensen was shown a straight red card for fouling Mane as he raced through on goal.
Liverpool took complete control of the match in a four-minute period after half-time, with Mane first heading the visitors in front.
Shortly after, Mane gave the ball away only to close down Arrizabalaga and block his attempted pass, before slotting home.
It was another horrible moment for the Chelsea goalkeeper, who has endured a nightmare spell at Stamford Bridge following his record-breaking move from Athletic Bilbao in 2018.
Commentating on the match for Sky Sports, former Manchester United and England defender Neville said: ‘Kepa, well, we know his fate. There’s no point deliberating it any further.
‘I thought Kepa got away with it with the red card. He should not have been out there. Mane would have gone around him and scored.
‘It’s a real problem if you’ve got a goalkeeper making errors. The anxiety it creates in the team is really bad.’
Neville also hailed Mane for his reaction to losing the ball in the build-up to his and Liverpool’s second goal.
‘That’s an example of how to react after making a mistake [from Mane]. Liverpool’s work off the ball is brilliant to watch.’
After Liverpool went 2-0 up, Jorginho missed a penalty as Chelsea were condemned to their first defeat of the new season.