Sadio Mane reached 100 career goals for Liverpool in a 3-0 win against Crystal Palace that sent the Reds top of the Premier League, while Arsenal eased the pressure on Mikel Arteta with a battling 1-0 victory at Burnley on Saturday.
Defending champions Manchester City dropped two points at home to Southampton after a 0-0 stalemate while struggling Wolves lost their fourth match in five against 10-man Brentford.
Mane continued his eye-catching mastery of Palace, netting in his ninth league match in a row against the Eagles.
Mohamed Salah's glancing header from Kostas Tsimikas' corner was kept out by goalkeeper Vicente Guaita but Mane pounced to lash home, giving him a century of goals for Liverpool in all competitions.
Salah doubled the Reds' lead in the 78th minute before Naby Keita sealed the win with a sweetly struck volley.
Liverpool have made an impressive start to the season, scoring 12 goals in their opening five games and conceding just once.
"I told the boys that is one of the most hard-fought 3-0 wins I ever saw. We gave everything," Liverpool boss Jurgen Klopp said.
"Sadio's 100th goal for Liverpool, a massive mark! It was a really good game for Sadio. He worked incredibly hard again."
Arsenal were rock bottom of the table before last week's fixtures but wins against Norwich and now Burnley lifted them to the relative comfort of 12th spot before the late kick-off between Aston Villa and Everton.
Odegaard, who signed from Real Madrid last month after spending part of last season at the Emirates on loan, broke the deadlock in the 30th minute, curling home a free-kick to give the visitors a 1-0 lead at Turf Moor.
Arsenal breathed a sigh of relief when VAR overturned a penalty awarded to Burnley in the second half after Matej Vydra tumbled to the turf following a challenge by goalkeeper Aaron Ramsdale.
"It was a hard-fought victory at a really tough place," Arteta said.
"We have players who are not at their strength playing in this type of game, but they did their best. I'm very proud of them defensively."
- CITY DROP POINTS
Manchester City will rue their inability to beat Southampton at the Etihad after consecutive 5-0 home wins.
It could have been worse for them after referee Jon Moss pointed to the spot when Kyle Walker bundled into the back of Adam Armstrong in the area, showing the England international a red card.
But the incident was reviewed by VAR and Moss eventually decided to overturn both decisions.
The build-up to City's match was dominated by a row over attendance levels at the Etihad, with manager Pep Guardiola urging fans to fill empty seats in comments that irritated some supporters.
But fans were frustrated by battling Southampton, who kept City's attackers at bay despite relentless pressure.
The home side thought they had snatched victory in the dying minutes after goalkeeper Alex McCarthy saved a Phil Foden header and Raheem Sterling tucked in the rebound but the flag was raised.
"We were not good in our build-up and lost the ball because we were not clever today and a bit sloppy," Guardiola said.
"It is because we didn't do our process with the back four and Fernandinho. Those five players have to bring the ball forward for the others."
Watford beat Norwich 3-1 to condemn the promoted Canaries to their fifth consecutive defeat.
Watford took the lead in the 17th minute through Emmanuel Dennis but Teemu Pukki equalised before halftime. Ismaila Sarr put the visitors back in front in the 63rd minute and scored again with 10 minutes to go.
In the early kick-off, Ivan Toney scored a goal and created another as 10-man Brentford beat Wolves 2-0 to maintain their impressive start to their first Premier League campaign.
The 25-year-old striker won and converted a penalty before setting up Bryan Mbeumo as the Bees prevailed at Molineux despite Shandon Baptiste's red card in the second half.
Tottenham host Chelsea on Sunday while Cristiano Ronaldo's Manchester United travel to West Ham.