The victory was the biggest of Emery’s reign to date with the Spaniard, who arrived in November with the team perched just above the relegation zone, hailing it the moment they definitively killed off any fears of the drop.
Villa have taken 26 points in 14 matches under Emery and now sit just four points behind sixth-placed Liverpool, with matches against Chelsea, Brentford and Fulham to come after the international break.
Emery said: “Today, maybe we can feel we are completely safe from the bottom teams.
“That was the first thing because when I arrived we were struggling more at the bottom.
“Now we can add a new step and objective looking at the teams in the top-10 now. They have an advantage over us and we have to fight, starting behind them as well.
“But we are going play here against Fulham and Brentford. We are going to play Chelsea in the next match and of course, it is going to be very difficult.
“But we are going to try and add a new target in our minds.”
Douglas Luiz, Jacob Ramsey and Emi Buendia got the goals as Villa put the relegation-threatened Cherries to the sword, recording the second successive home clean sheet in the process.
Owners Nassef Sawiris and Wes Edens were in attendance to enjoy the performance and Emery said: “It was the first time since I was here they were both here. I appreciate the visit a lot, the players the same.
“It is good to be together here. Today was a really good day because they watched our victory and enjoyed it.
“They are the owners, we are the professional coaches and players but the supporters, they are the real owners of the club.
“We have to be together, trying to do something. In the beginning it is trying to do good work.”