Hendrick finished superbly to win a game that looked to be heading for a draw when he swept a right foot shot from the angle of the box into the top right corner of the Rotherham net in the 82nd minute.
It was tough on the visitors who grew into the game after Derby had threatened to blow them away in the opening 20 minutes and saw a goal-bound header from Karl Arnason cleared off the line by Will Hughes.
Matt Derbyshire headed wide from eight yards before Hendrick pounced but Rotherham twice came close to equalising in stoppage time with former Derby midfielder Paul Green forcing a superb save from Lee Grant and Kieran Argard having a shot cleared at full stretch by Craig Forsyth.
But Hendrick's quality was the difference and McClaren believes he can repeat last season's double figure goal tally by midfielder Craig Bryson.
"Absolutely," McClaren said. "Keep your eye on Jeff. He played really well in the last 10 games of last season and that was a great finish today.
"He's got a goal threat, he's box to box, strong and tough and he's got everything which he's proved again today. He kept his head and got the winner when it didn't look like it was going to come.
"Credit to our players, they have got through on character after the first 25 minutes when I thought we were excellent. We got a little frustrated and lost our patience a bit and I thought it was heading for a draw but we have that quality to win games which we did in the end."
Rotherham manager Steve Evans thought his team was worth a point on their return to the Championship.
"I think Derby supporters will go away and know their team was in a tough game today," he said.
"They will have a lot of easier games at the iPro, that's for sure. I think we deserved a point and I think the whole ground knows we deserved a point but sometimes you don't get what you deserve.
"Many people around the country thought when they saw we were away at Derby it would be lambs to the slaughter but we aren't going to be lambs to the slaughter for anyone.
"We were well organised and after they scored, we had two great chances to equalise we would normally take so we are disappointed we didn't take them but we're learning."