The win moves the North London side up to ninth spot, level on 14 points with sixth-placed Manchester United, and there were real signs that manager Mikel Arteta is finally putting together a side with prospects.
Emile Smith Rowe delivered another excellent performance on the left of midfield, capping his display with the third goal, but there was a good shape and confidence to the entire team.
A Smith Rowe corner led to the opening goal with Thomas Partey's attempted headed glancing off his shoulder and going in the far corner to give the Gunners' a 23rd minute lead.
Bukayo Saka should have made it 2-0 when he was put in on goal but his first-time shot was straight at Emiliano Martinez who kept it out with his legs.
The hosts doubled their advantage before the break with Pierre-Emerick Aubameyang driving home after his penalty was saved by Villa's former Arsenal goalkeeper Martinez.
Referee Craig Pawson gave the penalty following a VAR review in added time after Villa defender Matt Targett went through the back of Alexandre Lacazette's legs.
Smith Rowe made it 3-0 in the 56th, finishing a well-worked counter-attack by cutting in from the left and seeing his low shot go in off the post after a deflection off Tyrone Mings.
Arsenal keeper Aaron Ramsdale did well to keep out an effort from Villa's Argentine midfielder Emiliano Buendia from a rare attack by the visitors.
Villa had been second-best for most of the game but pulled a goal back eight minutes from the end when Jacob Ramsey curled the ball into the top corner after Leon Bailey had burst across the front of the penalty area.
Arteta had been disappointed with his side's 2-2 draw at home to Crystal Palace but was delighted with the reaction from his team.
"We attacked them really aggressively, we won every duel. We were creative, a threat. I'm proud of the team, they played really well," he said.
"This is how we have to play. This is when we are good, when we play with real desire, real commitment and can have clear ideas of how to attack them. We are closer together as a team," he added.
Villa boss Dean Smith was disappointed with his team's first 45 minutes.
"It was a very poor first half. Not recognisable as a Villa team we have come to know. They deserved what they got. We got dominated physically. If we had got through the half at 1-0 I would have fancied us, but 2-0 was hard to get," he said.