Though there are certainly milestones in the development of "3D" engines, it has been a slowly developing trend for MUCH longer.
The very first "3D" commercially successful games stem from way back in the early 80s (likely earlier than that), with arcade wireframe games like Star Wars and stuff like that. The pursuit started long, long ago.
While Doom was most definitely one of the truly impressive games of its era, you can hardly mention it without giving credit to Wolfenstein 3D which was id's first mega hit, and of which the Doom engine was an evolution.
It should also be mentioned, that Doom wasn't a true 3D engine, because you couldn't look up or down, and much of what you saw as 3D were in fact "tricks".
The first generally accepted true 3D gaming engine (with textures) was actually Quake, though a few things like parts of torches were still sprites. System Shock (1994) had a very elaborate 3D engine, but used sprites for enemies and certain other stuff.
A couple of games were instrumental in promoting video cards with dedicated 3D acceleration hardware, and among the biggest of these were Tomb Raider and Quake. Quake 2 came later when 3D cards already had made their major breakthrough.
3DFX (makers of Voodoo cards) were the first "victors" in the 3D card war, but they were not the only ones producing cards. I personally had a 3D Blaster (Rendition chipset) card a while before the first Voodoo card was released, and I remember how much in awe I was running Quake with accelerated 3D hardware.
That was before the term "GPU" was invented or at least commonly used, by the way.