Within two minutes he took part in a move that saw Jonny Russell claim he was fouled on the edge of the area - but nothing was given.
Derby continued their early pressure and Craig Bryson fired over before Leicester striker Vardy forced a save from Grant with a drilled effort.
The Foxes broke the deadlock courtesy of Coutt's botched clearance after Liam Moore headed down a corner, and they had a chance to double their lead when Chris Wood was thwarted by a great tackle from Richard Keogh.
Schmeichel denied Freeman an equaliser before Grant saved from Vardy again. Keogh also headed wide as Leicester held on to end Derby's unbeaten start to the season.
Derby manager Nigel Clough:
"We had a great start to the game. We were on the front foot and were creating chances and then around the time of the goal they came back into it. But 10 minutes into the second half, I thought we controlled the last 30 minutes and played some very good stuff.
"There were lots of nearly moments in the game for us but I thought it was a good enough performance to get something and if you deal with the corner, the bare minimum you come out with is a 0-0 and you keep the unbeaten run intact and move on.
"I think defensively they are one of the best sides and one of the most difficult sides to score against but we certainly had enough situations that we didn't quite turn into chances but we had enough in the second half to get a goal.
"We are OK, we are in good spirits. We know we've played well again and we are happy with the squad and the way we are trying to play. We've had a little setback and we will use that as an incentive to try and go on an unbeaten run before the international break."
Leicester City manager Nigel Pearson:
"We've started the season OK but performance wise we still have a lot to do.
"We didn't play particularly well today, I think Derby managed the ball very well but ultimately we've come away with the three points. I'm not going to moan too much but we are a lot better than that.
"I look at the positives, it's a clean sheet, we've won, there's room for improvement and it's nice to get two away wins."
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