It wasn't just the oil exports that made the USSR part of the global economy, and let's not forget that the USSR was at the head of it's own economic bloc, COMECON, with plenty of third world client states. So it was hardly isolated.
Well I might have put it differently. What I meant is that during the 70s both USSR, and its eastern European neighbors became sensitive to the disturbances on the capitalist markets. USSR, mainly trough its massive oil exports, and other countries by actively participating in the global capital market, via MMF etc...
The structure of USSR exports within COMECON changed dramatically during this time as well. If you take a look at the figures, you will see that during the 60's large portion of USSR exports, to Eastern Germany, where finished goods, in the early eighties, they where importing finished goods, and exported mostly oil and gas...
I believe, that by it self reliance on oil, was just one of the factors. I think that the core problem with the centrally planned system was that it was utterly inflexible, incapable of quick response to external pressure from capitalist economies, and more important, unable to switch from industrialization model, relying heavily on cheap labor, and unable to implement industrial innovations (outside the defense industry).
On top of it all, the economic crisis would not have torn USSR-down, by it self -- no matter how harsh it was, without ill conceived political and economic reforms in Gorbachev era. As former CIA head put it: if Andropov was 15 years younger, USSR would probably be still around (poorer, lagging in the development, more autocratic, but it would probably survived.)
So, taken together, there where a lot of factors in USSR dissolution, some of them far more important than, simply, undiversified exports, and oil reliance, but that one was not insignificant either.