Both goalkeepers excelled early on to keep the contest scoreless in what was a frantic first period.
Villa began the second half in the ascendancy and seemed the more likely scorers, but failed to trouble Tim Howard as frequently as before.
This proved costly when Lukaku stroked home a clinical finish on 68 minutes, following a well-worked move involving Leon Osman and Leighton Baines. Osman then sealed the points 13 minutes later, hitting home Gareth Barry's clever lay-off.
The win temporarily elevates the Toffees to third in the table, after their fifth triumph in six games.
Here's a look at a few Everton-related talking points to emerge from this contest.