The League One side started the better with a series of counter-attacks and were very much on top in the early stages.
On 23 minutes they should have taken the lead when after terrific run by Deane Smalley was ended by a trip by Rory McArdle.
The resulting spot-kick by Lee Hughes was brilliantly saved by Rochdale keeper Sam Russell.
This lifted the home side and they began to enjoy the better of the exchanges before a rare flash point just before the break saw Davies dismissed for a head butt on Nathan Stanton right under the nose of referee Webster.
With his usual refreshing honesty, Oldham boss John Sheridan described his actions as "stupid".
The remainder of the game saw the League Two side camped in the Oldham half creating a series of chances that they didn't or couldn't take.
The nearest they came was on 53 minutes when veteran keeper Mark Crossley produced a stunning reaction save to keep out a header by Chris Dagnall.
The penalties saw Neal Eardley for Oldham and Tom Kennedy for the home side score convincingly, but after Chris Taylor had blasted his home for Oldham, Rochdale striker Dagnall blazed over.
Danny Whitaker calmly slotted home his spot-kick before Crossley saved the next effort from Dale's Adam Le Fondre leaving Lee Hughes to add the coup de gras.