The Reds last suffered defeat on January 3 last year in a 2-1 loss to Manchester City and, on the day before the first anniversary of that reverse, they had little difficulty dispatching the Blades to ensure they pass that marker.
Jurgen Klopp was forced into a pre-match change when Naby Keita suffered a groin injury, though it seemingly had little impact as Liverpool were ahead by the fourth minute thanks to Salah.
The solid performance of Manchester United-owned goalkeeper Dean Henderson – who was also aided by the post in the second half – helped keep the score down, but Mane wrapped the win up in the 64th minute at the end of a blistering move to restore Liverpool's 13-point lead at the Premier League summit.
The Reds were kept at bay for just four minutes, as George Baldock's slip allowed Andy Robertson to retrieve Virgil van Dijk's long ball and the left-back found Salah to convert.
Dean Henderson showed his quality soon after, however, producing a remarkable save to deny Salah a second as he turned Jordan Henderson's cross towards goal.
The left-hand post was the next object in Salah's way, as his teasing cross in the 61st minute missed everyone and came back off the upright – Dean Henderson grabbing it before it could then cross the line, though there was no stopping the Reds soon after.
Alisson quickly rolled the ball out to Robertson and he fed the ball up the line for Mane, who offloaded to Salah and received an incisive return pass into the box, before finishing past the goalkeeper at the second time of asking.
25 - Sadio Mané has scored 25 Premier League goals at Anfield since the start of last season - across the top five European leagues, the only two players with more at a specific venue are Lionel Messi (29 at the Camp Nou) and Kylian Mbappé (27 at the Parc des Princes). Guardian. pic.twitter.com/VN89M6DCpd— OptaJoe (@OptaJoe) January 2, 2020
United should have pulled one back late on, but Oli McBurnie could not get enough on Jack O'Connell's cross and Alisson stopped it just before it could cross the line.
What does it mean? Reds' run roars on
Although Liverpool last lost on January 3, 2019, their unbeaten run technically began nine days later with a 1-0 victory over Brighton and Hove Albion.
With their next Premier League outing not until January 11, they have only one more match standing in the way of their streak surpassing a full year.
Salah simply super
Liverpool's Egyptian star did very little wrong on Thursday. Were it not for Dean Henderson's excellence, he would have almost certainly got a hat-trick, while he also provided the pass that teed up Mane.
Baldock's bad day at the office
The match started poorly for Baldock, as his slip allowed Robertson to set up Salah for the opener in the fourth minute. He never really recovered, struggling with the Scotland international and Mane throughout.
Key Opta Facts
- Liverpool have accumulated 58 points from their 20 Premier League games this season; in English top-flight history, only Manchester City in 2017-18 (also 58) have had as many points at this stage of a campaign (assuming three points for a win all-time).
- Sheffield United have lost all six of their Premier League matches against sides starting the day top of the table, including both meetings with Liverpool this campaign.
- Liverpool scored in their 29th consecutive game in the Premier League; only two teams have ever recorded a longer scoring streak in the competition - Arsenal between 2001 and 2002 (55) and Manchester United between 2007 and 2008 (36).
- United have lost back-to-back league matches for the first time since they lost both of their opening two games of last season's Championship.
- Salah became only the fourth player to score 50+ left-footed goals for a single side in the Premier League, after Robbie Fowler (85 for Liverpool), Ryan Giggs (83 for Manchester United) and Robin van Persie (63 for Arsenal).
- Alisson made his 50th Premier League appearance for Liverpool and kept his 26th clean sheet; among goalkeepers in the competition's history, only Petr Cech (33) and Pepe Reina (28) had more shutouts in their opening 50 starts than the Brazilian.
Liverpool host Everton in the FA Cup third round on Sunday, when the Blades host non-League Fylde in the same competition. Both sides return to Premier League action the following weekend – the Reds going to Tottenham, while United welcome West Ham.