When West Brom last won away from home this season, victory at Norwich City on 1 October put them fourth in the table under Ryan Mason.
The dismal run that followed – which was headlined by 10 defeats away from home - cost Mason his job in early January, leaving his replacement Ramsay faced with the prospect of overseeing a record-equalling league defeat in what was his first match away from home.
Both sides made five changes for the game, with goalkeeper Jacob Widell Zetterstrom among those coming in for the Rams after illness ruled him out of Tuesday's win at Charlton.
The Baggies' 5-0 home thrashing by Norwich the same night prompted an overhaul for the trip across the Midlands, which included O'Leary being given his debut in goal just a day after joining from Bristol City.
It would become a forgettable first appearance from the 29-year-old, whose failure to deal with a free-kick from Callum Elder saw him drop the ball in front of United States international Agyemang to pounce on.
The 44th-minute goal came from Derby's only effort on goal of an underwhelming first half in which Jayson Molumby tested Zetterstrom at the other end before George Campbell crashed a header just wide.
Both sides carved out opportunities inside the 90 minutes, with the best of them put well wide by Derby's Ben Brereton Diaz after linking up with Agyemang on a quick counter attack.
West Brom piled forward in search of an equaliser, and it was an effort from Josh Maja that squirmed just wide in stoppage time that eventually led to the leveller.
From the ensuing corner, Mepham's header at the back post proved too powerful for Zetterstrom to stop from crossing the line.
While West Brom managed to ease their woes away from home by collecting a much-needed point at Pride Park, the trip may prove costly after Karlan Grant went off early with an apparent hamstring injury while Krystian Bielik's night was ended by a shoulder problem.