Ross Barkley showed some early trademark bursts as the visitors started brightly, but he was denied a shot at goal by some good defending.
The game failed to find any sort of rhythm in a tame opening 45 minutes which ended goalless, however, leaving Toffees boss Roberto Martinez with some thinking to do at the break.
Following the restart, the Premier League outfit emerged much the stronger - largely due to their nine changes - with Kevin Mirallas making the pressure count.
The Belgium international made the most of McAleny's pass, rounding the keeper and tucking home to open the scoring at the County Ground.
McAleny, who is looking to make a breakthrough at Everton this term, was again involved in the second, playing in Romelu Lukaku who in turn found compatriot Mirallas to tap home a second.
There was a worrying sign for Martinez when Mohamed Besic limped off the field 20 minutes from time, but there was no doubting the scoreline as Lukaku latched on to another smart McAleny pass to add a third, before he notched a well-deserved goal of his own.