The Foxes could have doubled their advantage when Riyad Mahrez raided down the left and his ball into the box was turned just over the bar by Vardy.
Blackburn found an equaliser just before the break when Matt Kilgallon headed home a corner from the right from Corry Evans's delivery.
After the break, Leicester should have regained the lead when Vardy picked up the ball and raided into the box. He rounded Robinson, but his effort hit the post and the rebound evaded Nugent by inches.
Again, Blackburn pressed back and Craig Conway beat De Laet down the left and lifted a cross into the box for Rhodes, but his header went just over the bar.
Both sides tried to get a late winner, but were unable to find the net again as the match ended all square.