Van Nistelrooy's honeymoon period looked like coming to an abrupt halt as the Seagulls cruised into a 2-0 lead at the King Power thanks to goals from Tariq Lamptey and Yankuba Minteh.
The veteran Vardy proved he is still the Foxes' main man by levelling in the 86th minute and then turning provider for Bobby De Cordova-Reid's 90th-minute equaliser.
"If you are on the scoresheet and make an assist, then you have to say this result would not be possible without him," he said.
"It's also the performance of the whole team, of course, that puts him in position.
"I enjoyed the whole sequence leading up to the goal. And that's why we as a team, we put him in a position there.
"And that's why we want these players who can make the difference for us in position.
"Then Jamie had the awareness for that second goal. Because I think you know with strikers, their eyes are focused on the goals.
"But to have the awareness to play the path to Bobby, pretty good skill, that was a brilliant moment, because so late in the game, 90th minute, on the top of my head.
"And when you have the calmness and the composure to decide on these things, then that's absolute top class. We're happy that we have that.
"If you don't pass it, you have to score. I think he made sure that we were going to get that goal."
The result will feel as bad as a defeat for Brighton, who were in total control and missed the chance to move up to fifth in the table.
It is the second time this season they have let a 2-0 lead slip to late goals and boss Fabian Hurzeler says his side need to be more "mature".
"I think when you are 2-0 up and control the whole game, you don't give away too many shots for the opponent, and then things happen in 10 minutes, you should be disappointed," boss Fabian Hurzeler said.
"We got punished for easy mistakes. I think it happens now several times in the season so we need to learn.
"We need to find the right game management in this period of time to take away the three points.
"But in the end, I think it's it's our fault, it's our responsibility. We need to be much more mature.
"We need to be much more clear how we solve the things in the last five, six minutes, and then these things won't happen."