Henrikh Mkhitaryan and Alex Iwobi provided the creativity for the away side, and Emery elected to use a back three.
The Spaniard was pleased to see his Arsenal side return to winning ways as Pierre-Emerick Aubameyang hit the deciding goal at Bournemouth.
The Gunners have extended their unbeaten run to 17 matches but they had drawn their last three Premier League fixtures.
Aubameyang slid in to tuck home and seal a 2-1 win after Joshua King had equalised for Bournemouth following a remarkable Jefferson Lerma own goal.
AFC Bournemouth v Arsenal – Premier League – Vitality Stadium
Image credit: PA Sport
Arsenal have not tasted defeat since August and are now just a point outside the top four – with Emery happy with the display on the south coast.
“Today is 17 matches we haven’t lost, but the last three matches we drew,” he said.
“We know that is not enough for us, for our objectives. We were speaking during the week and above all in the two days before the match that it was very important today.
“Today the three points is a big moment for us. The result is very important but also we spoke in the dressing room after the first half, when they scored, about the process in our mentality.
“The result is very important. When they scored we needed to keep calm and continue to control, getting better in small things on the pitch.
“We knew this is a difficult stadium, a difficult team. They were four points behind us and it was a very important match to be near us. I am very happy how the players, also the supporters pushed and helped us today.”
Emery reverted to a three-man defence for the first time in the league this season.
The Spaniard admits he is still working to find the best option at his disposal, with several systems to choose from.
“This is one possibility,” he said of a back three.
“We are finding our best performance with the system, with the players and with the combination. “We need the balance with some players. For the positioning on the pitch when we are attacking and defending and we tried to do that today.
“The most important thing for us 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.”
Meanwhile, Bournemouth boss Eddie Howe is keen for his players not to allow their morale to drop following a third successive defeat.
The Cherries lost to a last-gasp goal to Manchester United before a surprise reverse at Newcastle – with Arsenal’s win on the south coast continuing a small drop in form.
“It was the same with Man United,” Howe replied when asked if there was any consolation in running Arsenal close.
“We took them to the limit and came away beaten in that match. It was the same today, it is very important that the players’ confidence level doesn’t get affected by those two defeats.
“But we have had a very strong start to the season. It is important we don’t overreact in these moments and keep doing what we are doing and know we will win again soon.”