The Egypt international pounced on an errant touch from Eric Dier to open the scoring with a third-minute strike against Tottenham on Sunday at Anfield.
It was Salah's 20th goal for Liverpool in 25 league matches since his summer move from Roma.
25 - Mohamed Salah has netted 20 goals in just 25 games in the Premier League; the fewest appearances of any Liverpool player to reach 20 goals in the competition. Lightning. pic.twitter.com/zwMvDfhrdA — OptaJoe (@OptaJoe) February 4, 2018
In hitting that total, he did so faster than any other Liverpool player — besting the 27-match pace set by Torres and Sturridge.
The 25-year-old scored his 21st goal in second-half stoppage time, netting an impressive individual effort that appeared to give Liverpool all three points before Harry Kane's last-gasp penalty earned a 2-2 draw for Spurs.
Salah now ranks fourth all-time for goals scored in the first 25 Premier League matches for a club, tied with the Newcastle duo Alan Shearer and Les Ferdinand.
Sunderland's Kevin Phillips holds that record with 24 goals, followed by Newcastle's Andy Cole on 22 goals.
Salah has 28 goals through 34 matches in all competitions for Liverpool this season, having scored six times in the Champions League and added one more in the FA Cup.