Roberto Martinez's men had only managed a single triumph in seven league games prior to Villa's visit to Goodison Park, but they rarely looked like dropping points on this occasion.
Phil Jagielka, Romelu Lukaku and the returning Seamus Coleman were on target as the hosts controlled proceedings and produced some enterprising football on their way to a morale-boosting success.
Although Villa were without Fabian Delph due to a dislocated shoulder, Paul Lambert was able to recall Christian Benteke and captain Ron Vlaar following their respective lay-offs.
Neither man was able to make much of an impact, however, and Everton led at the break through Jagielka's 18th-minute header before Lukaku and Coleman put the result beyond doubt.
Everton saw out the match in straightforward fashion, completing a first Premier League win at home since beating Manchester United in April and consigning Villa to a fourth successive defeat.
Martinez said Villa were the last team he wanted to be facing at home following their wins at Stoke City and Liverpool, but he received the boost of being able to welcome Coleman, Ross Barkley and James McCarthy back from injury.
The England midfielder looked particularly dangerous in the early stages, pulling the strings for his side and forcing Brad Guzan into a fine save from 20 yards in the 17th minute.
Guzan may have been able to keep his side level on that occasion, but Villa found themselves trailing less than 60 seconds later.
Baines' teasing right-footed delivery across the face of goal was too inviting to be missed and Jagielka nodded it in from point-blank range.
Villa grew into the contest as the first half progressed, but struggled to provide Benteke with service in the Belgian's first start since March.
Everton should have made the most of Villa's troubles by doubling their lead just before the break, as Coleman – back from injury in place of Tony Hibbert – cut into the area and saw his left-footed drive palmed away by Guzan.
The home side may not have been completely comfortable in the lead-up to half-time, but Villa were left with a much tougher task on their hands three minutes into the second period.
Lukaku collected a throughball from Barkley, held off Tom Cleverley and then saw a low effort squirm under Guzan, who will feel he should have done better.
With Villa desperately searching for a way back into the contest, Everton demonstrated quick thinking from a free-kick to grab a third goal with 14 minutes remaining.
After being released down the left, Baines fired a devilish cross into the six-yard box that Coleman met with an easy tap-in.
That ended any hope of a Villa fightback and Martinez will hope his side can now kick on as they aim to bounce back from a poor start to the league campaign.
