The Wales international right-back punished the visitors for careless defending in a game which featured few real goalscoring chances for either side.
The conditions made it difficult to play good football, but Oldham coped the better and deserved a result which gave their play-off hopes a welcome boost.
John Sheridan's team have steadily climbed the League One table with this win completing back-to-back victories at Boundary Park after Saturday's defeat of Tranmere.
They are prospering despite massive injury problems which deepened even further when key midfielder Mark Allott pulled a hamstring just before kick-off and had to be replaced by Jean-Paul Kalala, who was himself short of match fitness.
Oldham dug deep on the few occasions that their defence came under pressure and sentenced Bournemouth to a defeat which left the Cherries needing a minor miracle to avoid the drop.
Bournemouth made the brighter start and striker Jo Kuffour turned on the edge of the box before blasting his shot beyond the far post.
Sam Vokes headed a right-wing cross at veteran keeper Mark Crossley, but Oldham made the vital breakthrough on 24 minutes.
Gary McDonald was shoved in the back by Marvin Bartley as they challenged for a free-kick at the far post and McDonald was sent sprawling to the ground.
Eardley, who also scored from the spot against Tranmere, stepped up to drill his penalty inside the right-hand post despite goalkeeper David Forde diving the correct way.
Forde beat away a shot from Leon Constantine before Bournemouth's closest call of the game came when Max-Alain Gradel hit a 20-yard free-kick which was deflected narrowly over the bar.
The second half was low on entertainment, but Bournemouth could not carve out any opportunities to draw level and they were killed off ten minutes from time.
Josh Gowling tripped Chris Taylor as the winger was darting past him round the outside and Eardley again beat Forde from the penalty spot.