Arsenal moved up to third in the Premier League table after a 1-0 win over Bournemouth at the Emirates Stadium, while Chelsea continued their fine away form with a 4-1 victory at Southampton. Brazilian defender David Luiz scored Arsenal's only goal of the game with a ninth minute header from a corner. Over at St Mary's Stadium, Tammy Abraham and Mason Mount celebrated their England call-ups by firing Chelsea to a convincing victory. Abraham opened the scoring with his eighth goal of the campaign, before Mason Mount doubled the visitors' lead in the 24th minute. Southampton halved the deficit through Danny Ings after half an hour, only for N'Golo Kante to restore Chelsea's two-goal lead 10 minutes later. Michy Batshuayi then came off the bench to score in the 89th minute to ensure a comfortable day's work for the reigning Europa League winners. Abraham has nine goals in all competitions for Chelsea this term, underlining why England manager Southgate is keen to get him action in a competitive match to ensure he commits to England. The 22-year-old striker has won two caps for England in friendlies against Brazil and Germany in 2017, but he had flirted with switching his international allegiance to Nigeria, who he qualifies for through his father. Another England call-up from the Blues' squad – the 21-year-old Fikayo Tomori – is also eligible to represent Nigeria, but the centre-back showed his England credentials with another composed display to keep Southampton largely at bay. Midfielder Mount, 20, again showcased the predatory instincts that have helped him make a smooth transition to the top-flight following last season's loan alongside Tomori at Derby County. On his week to remember, Abraham said: "It's been fantastic, I give it to my team-mates and my manager – everyone who has been behind me. When you play with great players you get your chances." Blues manager Frank Lampard. though, was determined to keep the result in perspective. "Let's not get carried away," he said. "It's a long season and we feel we might have picked up more points than we've actually got. We've not been at our absolute best and we can be a lot better. In north London, former Chelsea defender Luiz scored with a glancing header from a Nicolas Pepe corner, his first goal for the club. But that proved to be the only goal of a contest which lacked both chances and quality as Bournemouth managed to keep in-form striker Pierre-Emerick Aubameyang on the periphery. Cherries manager Eddie Howe said: "As bad as we were in the first half, we were good in the second. We dominated possession and deserved a point." Despite the victory, Arsenal manager Unai Emery admitted his side must be self-critical of their performance. The Gunners had just two shots on target and were lucky to survive in the second-half as Callum Wilson spurned a huge chance to equalise for Bournemouth. "We are very happy with that result. I'm very proud with our work in the first-half, but we are very critical with ourselves to improve things," said Emery. "We spoke before the game that if we'd win, we would be third in the table and for our confidence it was important. "Maybe in the second-half, we were winning 1-0, we were struggling more than we wanted and maybe in some moments we felt pressure." After the international break, Arsenal will face a trip to promoted Sheffield United in their next league assignment, while fifth-placed Chelsea will host Newcastle United.