But Chris Martin pulled one back from the penalty spot before the interval and the Cottagers capitulated after the break as goals by Johnny Russell, Jeff Hendrick and two from Simon Dawkins in a whirlwind 20 minutes sent the Championship leaders through.
"The goal just before half-time gave us a lifeline," said Rams boss McClaren. "And at half-time the players wanted to do something about it.
"The second half was more like us, we showed good character and played some good football. It was a devastating period."
For the big stories and the banter follow us on Twitter: @tribalfootball