The former England international bagged a brace to net for an eighth straight game and ensure the Foxes closed the gap on the Reds at the top to eight points.
Kelechi Iheanacho and Jonny Evans also scored to help Leicester set a new club record of eight consecutive top-flight wins.
Jack Grealish did make it 2-1 just before the break but the Foxes were rarely in danger.
Brendan Rodgers’ second-placed side are 14 points clear of fifth-placed Manchester United and refusing to budge in the title race.
In contrast, Villa sit 17th after they were thumped, slipping to a fifth defeat in seven games.
Before, the hosts remembered former boss Ron Saunders, who took them to the First Division title in 1981, after he died aged 87 on Saturday.
From the start, Villa were second best and James Maddison was foiled by Ezri Konsa’s block after just two minutes.
It was a warning Villa failed to heed during a first half where they were wide open and Leicester should have taken the lead after 10 minutes.
Caglar Soyuncu knocked Maddison’s deep free-kick back for Evans but, just four yards out, the defender stabbed at Tom Heaton.
Immediately, Villa broke to spurn their own golden chance when Matt Targett crossed for Anwar El Ghazi to rattle the bar from six yards.
With the chance went Villa’s early hopes and they swiftly lost any grip of the game when Vardy continued his scoring streak after 21 minutes.
Wesley lost the ball and the lively Iheanacho slipped the striker in to race clear and round Heaton.
The in-form Vardy miscued his kick when shaping to shoot but recovered to tap in, despite Konsa’s efforts on the line.
Vardy is now just three games away from equalling his own Premier League record of scoring in 11 consecutive games.
Villa’s problems were partly of their own making with Tyrone Mings unable to cover having already suffered a hamstring injury and the defender was immediately replaced by Bjorn Engels.
The hosts remained open at the back and Konsa blocked Vardy’s effort before Engels had to make a decisive tackle to stop Vardy teeing up Iheanacho.
The Foxes threatened at will while Villa could not handle Vardy’s pace and Iheanacho’s movement.
Villa were guilty of over-playing when they did go forward and were punished four minutes before the break.
There was a touch of fortune but Leicester deserved to double their lead when Maddison crossed and Iheanacho diverted in at the near post.
The Foxes were cruising but Grealish pulled a goal back in first-half injury time when he curled in from 16 yards after the visitors failed to clear a corner.
Leicester, though, wasted no time in restoring their two-goal lead four minutes after the break.
Evans escaped Villa’s defence and was left unmarked to thump in a brilliant header from Maddison’s corner.
The game was won although Maddison should have made it 4-1 after 67 minutes only to clip the post.
Harvey Barnes also fired over five minutes later and Vardy wrapped up the game when he raced onto Dennis Praet’s ball to roll under Heaton with 15 minutes left.
It was his 16th goal of the season and Soyuncu was denied a fifth by Heaton soon after as Leicester ran riot.