Manchester City had moved to the summit with a 3-1 victory at Crystal Palace earlier in the afternoon, but the Reds regained first position with a two-goal success over the Blues, who stay fourth in the division.
Jurgen Klopp's side are again two points clear of City, but the reigning champions do have a game in hand, meaning that the advantage is still with the Citizens.
There were no real surprises in the Liverpool XI, with the big decision perhaps seeing Naby Keita keep his spot ahead of Georginio Wijnaldum, while Joel Matip and Andrew Robertson returned to the side.
Chelsea's first serious attack arrived in the 12th minute when N'Golo Kante broke forward from midfield before finding Hudson-Odoi, but the England international's dangerous cross was punched clear by Alisson Becker.
Liverpool were the team forcing the issue in the first 20 minutes, but the visitors continued to have bright moments on the counter-attack with Loftus-Cheek bursting forward from midfield on a number of occasions.
Hazard tested Alisson in the 20th minute following another Chelsea break, before Jordan Henderson had a strike deflected just wide of the post down the other end seven minutes later.
Chelsea had another opportunity on the half-hour mark when Willian broke into a dangerous position just outside the Liverpool box, but the Brazilian fired his effort wide of the post.
Maurizio Sarri's side continued to cause problems on the break as the first half approached its latter stages, but Liverpool had a golden chance to take the lead in the 38th minute when Salah found Mane, only for the Senegal international to miss the target from inside the box.
An entertaining first period produced seven shots, but the two teams headed down the tunnel at 0-0 with City hoping that Chelsea could hold on for at least a point at the end of another 45 minutes.
Keita struck over the Chelsea crossbar in the early stages of the second period, but Liverpool took the lead in the 51st minute when Mane headed a clipped Henderson cross into the back of the net from close range.
The Reds then doubled their advantage two minutes later when Salah found space outside the box before picking out the top corner with a stunning strike for his 19th league goal of the campaign.
Roberto Firmino just missed the post in the 58th minute as the Merseyside outfit looked for a third, before Hazard struck the post for the away side down the other end of the field.
Hazard had another huge chance for Chelsea moments later, but Alisson kept out the Belgium international's close-range attempt, before Kepa denied Salah down the other end in the 65th minute.
Kepa then had to save from Firmino in the 80th minute as Liverpool threatened to score a third.
There was to be no late rally from Chelsea as the home side comfortably secured all three points, placing the pressure back on City as a fascinating title race moves closer to reaching its conclusion.
Liverpool will attempt to book their spot in the semi-finals of the Champions League on Wednesday night before travelling to Cardiff City in the league next weekend. Chelsea, meanwhile, will be looking to make the semi-finals of the Europa League on Thursday ahead of their next league clash with Burnley on April 22.
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Matip, Van Dijk, Robertson; Fabinho, Keita (Wijnaldum 66'), Henderson (Milner 77'); Mane, Firmino, Salah (Shaqiri 90')
CHELSEA (4-3-3): Kepa; Azpilicueta, Rudiger (Christensen 40'), Luiz, Emerson; Kante, Jorginho, Loftus-Cheek (Barkley 75'); Hudson-Odoi (Higuain 56'), Hazard, Willian