On-loan Derby hitman DJ Campbell was on the receiving end on both occasions as Posh's fight against the drop received another hammer blow as Derby won 3-0.
Steve Davies opened the scoring for the visitors from the penalty spot on the stroke of half-time and Campbell's second-half brace sealed matters.
Miller departed London Road to a chorus of boos despite neither manager condemning his two major decisions, while the defeated hosts were given a standing ovation.
Posh boss Mark Cooper said: "I'm loath to condemn either the referee or my players involved after only seeing the incidents once in the heat of the moment.
"If the first challenge was two-footed he certainly deserved to go but my initial reaction to the second was that Ryan got the ball.
"Those dismissals changed a ame in which we were playing really well and creating the best chances. Even when down to nine men our effort and commitment was absolutely first class.
"There is no getting away from the fact that the referee had a bad day on the whole. Unluckily for us, he chose to have it here."
Posh handed debuts to their four January loan captures - Kerrea Gilbert, Jake Livermore, Reuben Reid and Izale McLeod - but their arrivals were to no avail.
Derby boss Nigel Clough said: "There are all sorts of meetings before the start of a season when the categories for sending players off are discussed.
"And I think both of the incidents in this game fell into the relevant categories. Their player's feet were off the ground for the first red card and DJ was through on goal with only the goalkeeper to beat for the second.
"Obviously it was a big result for us. To go away and score three goals, collect three points and keep a clean sheet was very pleasing, although I don't think we played as well against nine men as we had against 11."
Miller pulled out the red card for the first time in the 28th minute after a two-footed lunge from Morgan.
Posh's woes worsened in first-half stoppage time when record signing Bennett was also given his marching orders after hauling down Campbell in the box.
Davies rubbed salt into Posh's wounds by sending goalkeeper Joe Lewis the wrong way from the resulting penalty before Campbell made the game safe in after the interval.
The frontman was at the centre of every major flashpoint in the game, going on to double the Rams' lead only three minutes after the restart by beating Lewis at the second attempt.
He then completed the scoring by heading home a cross from substitute Kris Commons 15 minutes from time.