The forward's cross was nodded into the back of the net by Alexis Mac Allister in a frantic opening at Goodison Park.
Everton had taken an early lead through Beto but were only in front for five minutes.
In teeing up Mac Allister, Salah broke a league record which had stood for over 30 years.
His assist was his ninth away from home in 13 Premier League matches this season to go with 12 goals on the road.
The combined 22 goal contributions in away Premier League matches surpasses Andy Cole's record tally from the 1993/94 season.
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Cole scored 12 goals and provided nine assists during that campaign for Newcastle.
As well as making history, Salah extended his stunning season in attack for the Reds.
The 32-year-old now has 14 league assists this term, along with 21 goals in the competition.
Across all competitions, meanwhile, he has 26 goals and 19 assists in 34 appearances.
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Salah's league tally of goal contributions is already his best since the 2021/22 campaign, which he trails by just one.
As a result, the Egyptian is set to enjoy his most productive season for seven years.
His debut campaign at Anfield in 2017/18 ended with 42 combined goals and assists in 36 Premier League matches.
Salah is now just seven goals and assists behind that number with three months of the season remaining.
It could yet be his final year on Merseyside, though, with his contract due to expire at the end of the season.
The former Roma man has yet to agree terms on an extension to the deal he penned back in 2022.
During his time with Liverpool, Salah has already won eight trophies, including the Champions League, as well as three Premier League golden boots.
More silverware could still follow this term, with Arne Slot's side into the final of the Carabao Cup and cruising through the opening phase of the Champions League.
The Reds also sit top of the table domestically, with nearest challengers Arsenal six points behind prior to the Merseyside Derby.
More to follow.