Leicester opened the scoring in the 20th minute when Kelechi Iheanacho played in Vardy, who scored at the second attempt after scuffing his initial effort and moved within three of his PL-record goalscoring streak of 11 matches.
It was 2-0 after 41 minutes, with Iheanacho diverting James Maddison's cross in at the near post.
Jack Grealish pulled a goal back on the stroke of half-time with a deflected effort.
Jonny Evans made it 3-1 on 49 minutes, heading in superbly from Maddison's corner.
Vardy added a fourth with 15 minutes remaining, latching on to Dennis Praet's long pass to finish low past Tom Heaton.
Second-placed Leicester are now six points clear of Manchester City in third and eight behind leaders Liverpool.
Villa are 17th with 15 points.
Aston Villa: 14 Dec v Sheff Utd (A)
Leicester: 14 Dec v Norwich (H)