The Egyptian moved ahead of the Chelsea legend after he became the first Reds player to score a hat-trick at Old Trafford in the top-flight.
Salah's treble followed Mane recently hitting his century in all competitions for the Reds last month, helping the club to a 3-0 win over Crystal Palace at Anfield.
And the 29-year-old then brought up his 100th Premier League goal, scoring the opener in Liverpool's trip to Watford last week.
Mane thought he had scored his first in England's top-flight in Southampton's historic 8-0 win over Sunderland back in 2014.
However, his effort was later credited as a Patrick van Aanholt own-goal leaving Mane to wait another week for his maiden Premier League strike which came in a 1-0 home win over Stoke.
The winger - who also scored on his Liverpool debut - is now the third highest African goalscorer in Premier League history.
Salah meanwhile has bagged the bulk of his strikes under Jurgen Klopp, but the forward's first effort came during his time at Stamford Bridge.
Salah, 29, scored as a late substitute in Chelsea's 6-0 win over London rivals Arsenal in Arsene Wenger's 1,000th game in charge in 2014.
The ex-Roma star has now overtaken a Blues icon in his successful quest to become the highest African goalscorer in Premier League history.
Ivory Coast legend Didier Drogba is now three goals behind Salah having netted 104 times in 254 appearances over two spells at Chelsea.
Emmanuel Adebayor is fourth after spells at Manchester City and north London rivals Arsenal and Spurs while Everton hero Yakubu is fifth.
Alergia's Riyad Mahrez has a steep job hoping to break into the top five and is now level with Gabon striker Pierre-Emerick Aubameyang.