Naby Keita gave the Reds the lead after just 15 seconds after dispossessing a careless Jon Gorenc Stankovic almost straight from kick-off.
Mane then scored an almost identical header to stretch the lead to four, before Salah grabbed his second courtesy of a fine assist from Andrew Robertson.
The win moves Liverpool - albeit temporarily - above Manchester City while there is no mercy for the relegated Terriers.
Check out our player ratings in the gallery above.
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