For a team and manager both associated with slow starts, Martinez's side have displayed phenomenal form to begin the season, and they added to their impressive early points tally as Romelu Lukaku and Leon Osman scored to give all three poitns to the Toffees.
The game featured Christian Benteke and Romelu Lukaku lining up for their respective sides, so with two physical Belgian strikers, the game was always likely to be decided in part by which man displayed his best form. But with both sides too reliant on direct balls to their dangermen, they appeared to cancel each other out in the first half.
Benteke initially looked to have the edge as Seamus Coleman had to resort to Judo to stop him getting onto the end of a ball in the area, with the Belgian stepping up for the penalty, but Tim Howard produced a fine save to keep the scores level in the opening minutes.
Once again, Benteke raced clear only to be denied by Howard with another excellent stop. Next it was Lukaku's turn to threaten, but Brad Guzan did well to tip his header over the bar, in a game that was increasingly becoming more the battle of the American goalkeepers than the Belgian strikers.
The second half closed down, with both defences dealing with the primitive threat, but Lukaku opened the scoring midway through the half. Leon Osman's fine run allowed him to square the ball to the Chelsea man, who finished smartly past Guzan at his near post to give Everton the advantage.
Villa had been more than equals in the game, but increasingly looked like they had no more ideas, and it was no surprise when Everton made it two, with Osman again cropping up with a cool finish from the edge of the area after being picked out by Gareth Barry.
That proved enough for Everton, as their opponents were unable to provide any more pressure after disappointingly fading as the game went on. Paul Lambert's side have shown plenty of promise this season, but they haven't quite had the points to show for it - today continued in much the same theme.