Arsenal manager Arsene Wenger has said his side's win at Bournemouth means they are still very much in the title race ahead of a "big game" against Premier League leaders Leicester next weekend.
Arsenal won 2-0 after goals in an 87-second span from Mesut Ozil and Alex Oxlade-Chamberlain ended a four-game winless run in the league.
They are still five points behind Leicester, who convincingly beat Manchester City 3-1 on Saturday, but can close that gap when they host the Foxes at the Emirates Stadium next weekend.
"It was a must-win game for us today. Leicester have made a big impression in the last week after their results. They suddenly become the favourite in the Premier League and it makes our game a big game," Wenger told the BBC.
"We had a strong start, with good finishing and we controlled the game. We beat a good side, it was three difficult points but three very important points for us because we had not won for a while. We lost a bit of our urgency in the second half. We lost the killer instinct to get the third goal and on top of that Bournemouth are physically a strong team."
The win puts Arsenal back above Manchester City into third place, still behind North London rivals Tottenham on goal difference.
Having led the league in January, Arsenal's title credentials had been questioned this past week after a 0-0 draw at home against Southampton on Tuesday when Wenger's men missed a host of chances.
But the Frenchman insisted his team have the mental strength to claw back the deficit.
"We have been in the title race and we are still in it. We cannot control people's opinion and we need to show that we believe in it. We have to do it," Wenger said in his postgame news conference.
"It is still a long way to go. Leicester City is a favourite and we have a big game at home against them and I hope we have enough quality and nerves to deal with that."
Wenger was also full of praise for Ozil, who thumped home the first goal with an emphatic finish after missing a couple of good chances against Southampton.
"He has added a fighting attitude today. It was a top, top, top performance from him today," Wenger said. "He scored with his right foot which is very interesting for us. If he scores with his right foot he will become even stronger."
Arsenal midfielder Aaron Ramsey, who helped set up Oxlade-Chamberlain's goal, acknowledged that Leicester's win had increased the pressure on Arsenal to respond.
"We needed it badly. We realised what Leicester did yesterday and we needed to close that gap and it was important to go back to winning ways," Ramsey said.
"There was no room for error today, and I think the boys responded really well. We have a big game against them next week, so I'm sure that will be on that everyone will be interested in seeing. But hopefully we can keep this winning run now that we're on."