While the Millers were second best in a scrappy first half, they came closest to scoring when Jamie Green’s cross fell to Taylor in the area, but Rochdale goalkeeper Frank Fielding parried his low shot.
The visitors took the lead in the 50th minute, Reid holding off Nathan Stanton in the area and creating space for himself before drilling a low shot past Fielding.
Taylor added Rotherham’s second in the 71st minute, cutting inside Tom Kennedy before curling a fine effort past the keeper.
Dale pulled one back when Adam Le Fondre headed home Nicky Adams’ cross in the 76th minute.
Rory McArdle conceded a penalty shortly afterwards for a foul on Taylor but Reid smashed his spot-kick against the crossbar. His follow-up header ended up in the net, but referee Mick Russell ruled it out for a push on Fielding.