On-loan Monaco midfielder Youri Tielemans got the Foxes on their way with a simple finish midway through the first half after being teed up by Vardy, only for Floyd Ayite to pull the Cottagers level with their first effort on target in the 51st minute.
As the Foxes looked to be heading for a frustrating draw in Rodgers' first game at the King Power Stadium, Vardy unleashed an unstoppable drive into Sergio Rico's bottom-right corner to reach 100 goals for the club - then followed that up with another cool finish four minutes from time to wrap up all three points.
Rodgers was fulsome in his praise of the 32-year-old - who became the seventh Leicester player to reach the landmark and first since Gary Lineker more than 30 years ago – taking time to highlight his all-round contribution.
"I care for him because he is an absolutely top-class striker," Rodgers told a media conference.
"I think the first goal we scored tells you everything because he is clean through for his 100th goal and he squares for Tielemans, who is getting into the box.
"That tells you everything about how unselfish he is and what a team player he is. I am very happy he is here because my teams always have a striker at the top who can press and understand the game.
"What has surprised me since I arrived is he is tactically very good and understands to start the press. He is a wonderful striker and scored two wonderful goals."
Other than a 20-minute spell at the start of the second period, Leicester were comfortably the more dominant side and Rodgers says he is already starting to see his vision of fluid, attacking football starting to take shape.
"I always like the players to be within 10 to 15 metres of each other," he explained.
"When the attacking players try what I am asking them to do and it breaks down there are players close enough to then go and win the ball back and counter press the game.
"You have Jamie up there but then you have the two attacking midfield players up there and the wingers to support them.
"When you have the potential these young guys have then it can be exciting. The guys connected the game well at times. With a lot more work and ideas then that will improve."