LONDON (AP) -- Manchester City finally rediscovered the kind of football that made it Premier League champion, just in time for this week's crucial top-of-the-table clash against Liverpool.
Paultheir Pogba and Manchester United are finally looking like old selves, too, although whether there's still time to launch a challenge for the Champions League spots remains to be seen.
City beat Southampton 3-1 on Sunday to end a run of two straight losses -- and three defeats in four matches -- while United overpowered Bournemouth 4-1 to continue its resurgence under caretaker manager Ole Gunnar Solskjaer.
Chelsea also held on for a 1-0 win at Crystal Palace to strengthen its grip on four place, while Burnley ended a three-match losing streak with a 2-0 home victory over West Ham.
City's title defense had looked in danger of collapsing completely during the busy festive period after surprising losses to Palace and Leicester, but Pep Guardiola's team found its attacking verve at Southampton thanks to two quick goals just before halftime. David Silva and Sergio Aguero scored for the visitors, who also benefited from a fortunate own-goal by James Ward-Prowse.
The win puts City back into second place, two points ahead of Tottenham but still seven behind leader Liverpool ahead of the Reds' highly anticipated visit to the Etihad on Thursday.
And according to Guardiola, the title race could be over after that game unless City wins.
"With the position of Liverpool, if we drop points then it is over, it is finished. It would be almost impossible," Guardiola said. "We are not here to send a message, Liverpool know what they have to do, we know what we have to do on Thursday."
For Pogba and United, the race for a top-four spot is only now starting to build up some steam.
Pogba scored two goals and added an assist as United put in another impressive attacking display under Solskjaer, who now has three straight wins since taking over from the fired Jose Mourinho -- with the team netting 12 goals in that span.
"Obviously it's different," Pogba said. "It's just a different style of play, we are more offensive I would say, so we create more chances, and a bit higher as well. ... That's how we want to play, we want to attack, the manager wants to attack, and that's what we do on the pitch."
The French World Cup winner, who had been relegated to the bench during the final weeks of Jose Mourinho's reign after falling out with the Portuguese manager, put United 2-0 up after 33 minutes before Marcus Rashford and Romelu Lukaku added a goal apiece at Old Trafford. Nathan Ake had given Bournemouth some hope by pulling a goal back for 3-1 just before the halftime break.
Pogba celebrated his first goal by performing a playful shimmy with his arms folded across his stomach -- a move that TV cameras revealed he had been practicing on the pitch before kickoff.
Pogba, though, insisted it wasn't a rehearsed routine.
"No, no, no, it's just coming," he said. "Everybody knows I love to dance. That's how I celebrate my goals."
The win puts United just three points behind fifth-placed Arsenal, but they remain eight points behind Chelsea in the final Champions League spot after N'Golo Kante secured a narrow victory at Palace.
After a frustrating first half for the visitors, Kante provided the breakthrough when he ran onto a ball over the top from David Luiz in the 51st minute, chested it down with his first touch and slotted the ball under goalkeeper Vicente Guaita with his second.
Olivier Giroud also had two well-taken strikes questionably ruled out for offside -- one in each half -- while Willian and Ross Barkley both hit the post for Chelsea.
Burnley got first-half goals from Chris Wood and Dwight McNeil against a surprisingly toothless West Ham side, giving the team only its second win since Sept. 30. Sean Dyche's side remained in 18th place, but now only trails Southampton on goal difference and is just four points from 14th in a tight bottom third of the table.