The Belgian scored his third goal of the season, with Phil Jagielka and Seamus Coleman also amongst the goals at Goodison Park on Saturday
Centre-back Phil Jagielka met a Leighton Baines cross to open the scoring in the first half.
Romelu Lukaku netted his third goal of the season after half time, combining with Ross Barkley, before Seamus Coleman wrapped up the points with less than 15 minutes remaining.
Villa were without Fabian Delph due to a dislocated shoulder, but 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.
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.