I think the turning-point was that flat-framebuffers and plenty of CPU-power for the first time eclipsed specialized 2d hardware (Amiga,Megadrive, Snes, etc).
Flat framebuffers and "powerful" CPU's also enabled easier software rendering (Doom/Duke) of 3d, compared to the Amiga where writing textured rendering for an Amiga is a PITA due to video memory layout with separted bitplanes spreading bits of each pixel into different memory locations (the total memory bandwidth reduction in 1985 by using 5 or 6 bitplanes became a fatal bottleneck at this point).
It wasn't really always full framerate though and the 2d chipsets did help in "classic" actiongames that were still much in the rage.
The Pentium further widened the gap, but at the same time consoles gained hardware 3d acceleration (PSX/Saturn/Jaguar) yet the Pentium could do graphics better in some respects (As shown with Quake).
Once 3d accelerators landed, PC's has more or less constantly been ahead apart from when it comes to price (and comfort/ease).