Arsenal cut the gap to the top three in the Premier League on Sunday while Jose Mourinho was sent off as Manchester United's recent home struggles continued, according to dpa. Alexis Sanchez scored twice and Theo Walcott got the other as Arsene Wenger's side beat Bournemouth 3-1 to cement their position in fourth place, three points off leaders Chelsea, and two behind Liverpool and Manchester City. "We got better during the game but Bournemouth played well," Wenger admitted. "They started with a high intensity. We had to improve our level in the second half and we did. Our players questioned themselves a little bit after a few draws but we have responded." Sanchez put Arsenal in front after just 12 minutes after a lax backpass by Steve Cook but Bournemouth equalized through a Callum Wilson penalty 11 minutes later after a foul by Nacho Monreal. Monreal made amends early in the second half when he teed up Walcott for a rare header and Arsenal put some added gloss on the scoreline when Sanchez scored the third in the 90th minute. Walcott celebrated his goal by cradling his arms after the recent birth of his second son. "It was a good team performance today," he said. "Bournemouth are a very solid team, they play very good football and we did find it difficult at times. We started to click again, even if it was in patchy stages, it's started to happen again." Mourinho was sent off for the second time in four games as United were held 1-1 at home by West Ham. Diafra Sakho put the Hammers in front after just two minutes with Zlatan Ibrahimovic equalizing in his return from suspension. Mourinho was then sent to the stands for kicking a water bottle after Paul Pogba was booked for diving. He also was dismissed during last month's 0-0 draw with Burnley. United had 68 percent possession and 17 shot attempts but couldn't avoid a fourth straight home draw that left them eight points off the top four in sixth place. "Another game the same," midfielder Ander Herrera told the BBC. "We control the game completely from the kick-off. They score a very lucky goal and then we control and create chances. We don't know what we have to do to win a game." Charlie Austin's goal after just 41 seconds gave Southampton a 1-0 win over Everton and former manager Ronald Koeman. Austin headed home from close range as the Saints ended ended a four-match winless run and moved up to 10th place, two points behind Everton in seventh. Stoke are up to 11th after a 1-0 win at Watford. An own goal by Huerelho Gomes in the 29th minute won it for Mark Hughes's side, who continue to pull away from trouble after a shocking start to the season. Hughes paid tribute to his players in what was a rejigged side due to a number of absences.