Vardy's introduction with 18 minutes to go was his first appearance of 2022.
With the score locked at 0-0 at the time, Vardy set up fellow substitute James Maddison for the opener before claiming the second with a header from a Harvey Barnes cross in the 90th minute.
The win was Leicester's first of 2022, propelling them to 12th position on the table.
Rodgers was delighted with the impact of his substitutes but reserved special praise for the returning Vardy, whose strike was his first in the league since November.
"We knew we had James [Maddison] and Jamie's quality to come on," Rodgers told BBC Sport. "James scored a brilliant goal and then you could see the confidence from it. Then Vardy was there and did what Vardy does best.
"He is a real catalyst for the team. You see his energy. He makes runs and presses and is normally in the right areas to score. He is a huge boost for us. To have that quality and mentality back in the team will help us.
"We have to stay focused on the football and not look too far ahead. Stay calm, play our football and keep focused and then we came here and got a result.
"A long way to go in the season. We want to go far as we can in the European competition and see where we are at the end of the season."
Vardy added:"The main thing was to get back on and put a performance in.
"You always want to come on but you always have to listen to the medical team as well and I've been back in training just the last four days. Getting 20 minutes it is good for myself there is no more issues.
"I don't think you can lose that [scoring touch]. It is instinct."
