At the bottom, there were crucial wins for Burnley and Cardiff City against Brighton & Hove Albion and Southampton respectively, while Wolverhampton Wanderers made it back-to-back victories by beating 10-man Newcastle United.
West Ham United edged a five-goal London derby against Crystal Palace on Saturday too, and the gameweek concluded in dramatic fashion as Everton rescued a last-gasp 2-2 draw with Watford on Monday night.
Here, Sports Mole selects its Premier League team of the week for gameweek 16.
Alisson Becker did not have a huge amount to do in the Liverpool goal during their win over Bournemouth, but he was once again a commanding presence and was as important to launching attacks as he was to stopping them for the new league leaders.
The importance of Liverpool's win was heightened even further by Chelsea's victory over Manchester City later in the day, and Cesar Azpilicueta was a key component in keeping the free-scoring champions at bay with a whopping 13 tackles at Stamford Bridge - seven more than anyone else on the park.
Azpilicueta is joined in the backline by teammate David Luiz, whose mercurial talents were caught on a good day both in defence and in attack, where he scored his side's second goal. Joining him at centre-back is another goalscorer, with James Tarkowski netting the only goal of the game for Burnley against Brighton.
Manchester United's form this season means that they have not often got a look-in for these teams, but they boast three representatives this week courtesy of their 4-1 victory over Fulham. The first of those is Ashley Young, who scored a rare goal and also helped himself to an assist to beat competition from Ben Davies and Everton hero Lucas Digne.
Juan Mata joins his clubmate in the XI having also registered a goal and an assist at Old Trafford, while Tottenham's Dele Alli was also amongst the goals with his side's second against Leicester City in Saturday's evening kickoff.
The pocket-size dynamo Lucas Torreira earns his place in the team for the second time in the space of three gameweeks having scored an acrobatic winner against Huddersfield Town, which is enough to beat clubmate Granit Xhaka and Chelsea's N'Golo Kante into the XI.
The standout individual performance of the weekend came from Mohamed Salah, who scored his second Liverpool hat-trick including two fine solo efforts to fire his side to the top of the table.
Tottenham's Son Heung-min scored one and created the other during his side's 2-0 triumph at the King Power Stadium, while Marcus Rashford went one better with a goal and two assists in United's comfortable win over Fulham.