Unai Emery says Arsenal needed to beat Bournemouth to relieve pressure ahead of next weekend's North London derby.
The Gunners will host Tottenham at Emirates Stadium live on Sky Sports next weekend on the back of a 17-match unbeaten run, but they were made to work for three points at the Vitality Stadium.
Arsenal were poor in the first half but went ahead through an astonishing own goal by Jefferson Lerma only to be pegged back by Josh King's injury-time equaliser. Pierre-Emerick Aubameyang struck a second-half winner to move them two points behind Chelsea in the race for the top four.
Emery said: "Every match is three points, and today it was very important to win and stay near Tottenham, Chelsea and Liverpool.
"I think Man City are very far ahead, but we want to concentrate on our progress, and that was important today - especially playing against Tottenham at home next week.
"We are happy with the result, but also the commitment over the 90 minutes with our control was good. This is how you can win, like today, and we needed to win because we had drawn three games in a row. We spoke about how we needed to win today, and we are under pressure."
Emery employed a back three for the first time since taking over, and it worked largely to good effect in Arsenal's first win in four games.
He said of the decision: "We are finding our best performance with the system, with the players and with the combination, for the positioning on the pitch when we are attacking and defending and we tried to do that today.
"The most important thing is to find the balance consistently in defensive moments, because we are conceding more goals than we want, and not to lose our good performance in attacking moments. We need to improve, we need more in this balance."
Catch the North London derby next weekend live on Sky Sports Premier League from 2pm on December 2.