Two minutes after coming on as a late substitute at Anfield, Willian whipped in an attempted cross from the right which floated over Liverpool goalkeeper Simon Mignolet and into the net.
Salah, who was outstanding for Liverpool, had put his team ahead in the 65th minute when Alex Oxlade-Chamberlain poked the ball away from a hesitant Tiemoue Bakayoko.
The Egyptian then pounced on the loose ball to fire past Courtois.
The result leaves Chelsea in third place on 26 points, eight behind leaders Manchester City who play on Sunday, while Liverpool are fifth on 23 points.
In other Premier League games also played on Saturday Jose Mourinho’s United bounced back from their surprise UEFA Champions League defeat at Basel in midweek to win.
It was their 39th straight home win in all competitions.
The win also meant the Red Devils equalled a 51-year-old record set by Sir Matt Busby, thanks to Lewis Dunk’s second half own goal.
“I think we were more spirit and heart than quality. My boys didn’t play well but they gave everything,” Mourinho said.
“For me probably Brighton deserve more than the result they got.”
Also, Tottenham’s bid to win the title for the first time since 1961 was left in tatters after a 1-1 draw with lowly West Bromwich Albion left them 10 points behind City.
Spurs have had mixed results at Wembley since moving into their temporary home while White Hart Lane is rebuilt.
But, once again, they lacked a cutting edge against supposedly inferior opponents.
“We weren’t clinical. It is always difficult in the Premier League when you concede a goal so early,” Pochettino said.
“I’m disappointed because the effort was massive, but we lost two points.”
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