Two goals in as many minutes from Sadio Mane earned Liverpool their first Premier League win of 2017 as Tottenham Hotspur were beaten 2-0 at Anfield.
Mane and Liverpool took full advantage of a chaotic first half from Spurs, who were unable to cope with the home side's intensity and offered far too much space.
The home side made the breakthrough after 16 minutes when Georginio Wijnaldum slid a superb pass through to Mane, who got away from Ben Davies to power a finish past Hugo Lloris.
Two minutes later, the lead was doubled when Tottenham's Eric Dier took too long to deal with a ball forward and was dispossessed by Mane. He set up Lallana whose shot was saved, as was Firmino's effort on the rebound, before Mane smashed home the loose ball.
Two goals from Alexis Sanchez -- one of them highly controversial -- gave Arsenal a 2-0 victory over struggling Hull City at the Emirates Stadium.
After a frenetic opening half hour that brought chances for both sides, Sanchez broke the deadlock on 33 minutes when the ball cannoned in off his hand following a scramble near the Hull goalline.
Hull defender Andy Robertson said after the game that referee Mark Clattenburg had apologised to the visitors for allowing the goal to stand.
Sanchez saw his close-range effort bounce off goalkeeper Eldin Jakupovic after a Kieran Gibbs shot was only half-cleared, with the rebound hitting him on the hand and bobbling into the net.
Arsenal sealed the points in the first of four minutes of stoppage time when Sam Clucas was sent off for handling a header from Lucas Perez and Sanchez scored his second of the game from the spot.
Anthony Martial scored on his return to the Manchester United lineup as Jose Mourinho's men moved to within a point of neighbours Manchester City with a 2-0 win over Watford at Old Trafford.
Zlatan Ibrahimovic had a chance to give United the lead in the opening moments when a deflected Antonio Valencia cross fell to him, but he miscued his volley and saw it bobble wide.
Ibrahimovic was then denied by a fine save from Heurelho Gomes, but United broke through after 32 minutes when a low cross from Anthony Martial eluded the striker but fell for Juan Mata to sidefoot home.
Martial was in the thick of the action again when his low cross just failed to find either Henrikh Mkhitaryan or Ibrahimovic and Watford were able to scrape the ball away.
United keeper David De Gea was forced into action early in the second half when Mauro Zarate curled a free kick towards the top corner in a rare attempt for the Hornets -- and that spurred United into action as Martial cut back onto his right foot and struck his side's second goal with an hour gone.
West Bromwich Albion scored a stoppage-time equaliser to rescue a point in a 2-2 draw at West Ham United.
West Brom scored with their first attack when Nacer Chadli got clear to shoot past home goalkeeper Darren Randolph, and Salomon Rondon almost doubled the lead when his powerful volley crashed off the crossbar.
But the home side levelled after 62 minutes when Ben Foster made a superb save to tip a Manuel Lanzini drive onto the bar only for Sofiane Feghouli to tap home the rebound.
Foster made another fine save when home substitute Jonathan Calleri fired a low attempt across goal as Slaven Bilic's side but was unable to stop Lanzini as he produced a smart finish after 86 minutes.
West Brom, though, refused to give up and were rewarded when substitute Jonny Evans headed home from a corner.
Crystal Palace's relegation worries deepened even further as Joe Allen's goal condemned them to a 1-0 defeat at Stoke.
Stoke started purposefully against Sam Allardyce's struggling Londoners and had an early opportunity to break the deadlock when Peter Crouch flicked on to Marko Arnautovic, whose drive was stopped by Wayne Hennessey.
Palace hit back when Andros Townsend got away down the left and crossed for James McArthur, whose header went wide, but Stoke won it after 67 minutes when a fine move involving Arnautovic put Joe Allen in and he produced a cool finish.
Sunderland saw their hopes of building on the 4-0 win at Crystal Palace last weekend shattered by Southampton, who thrashed them by the same scoreline at the Stadium of Light.
They were the stronger side in the opening stages but failed to break through -- and Southampton made them pay on the half-hour when an inswinging free kick was bundled home by Manolo Gabbiadini.
Southampton doubled the lead through the same player in style just before the break as he turned beautifully away from his defenders to slide home his second and leave Sunderland with a mountain to climb.
Gabbiadini came close to notching a hat trick in the early stages of the second half when his shot was stopped by Vito Mannone, but Southampton ended their recent poor run in emphatic style when Jason Denayer put through his own goal and Shane Long struck a fourth late on.
Middlesbrough and Everton were unable to find a goal as both goalkeepers produced some fine stops in a 0-0 draw at the Riverside Stadium.
Everton started brightly, with home goalkeeper Victor Valdes quickly off his line to deny teenager Tom Davies in the opening moments.
Boro were struggling to muster much threat but could have opened the scoring when Adama Traore was crowded out in the penalty area, but they were soon grateful to Valdes again as he denied Romelu Lukaku, who had been put clean through.
Valdes continued to be the Boro hero in the second half, producing another excellent stop when Ross Barkley put Ademola Lookman through, while Everton's Joel Robles emulated Valdes when he produced an outstanding save from Rudy Gestede with four minutes left.