Actually, Quillen's proof did contain a fantastic new idea : Quillen patching.
It states that if P is a fg projective R[t]-module then the set of all f in R, such that (for localizations at the multiplicative systems {1,f,f^2,...}) P_f is extended from R_f (that is P_f = Q \otimes_{R_f} R_f[t] for a projective R_f-module Q, is an ideal of R.
Apply this to R=k[x1,...,xd] then the localization of P at the set of all monic polynomials in R[t] is a projective k(t)[x0,...,xd] module whence free by induction. But then P_g is free for some monic poly g in t.
Now take a maximal ideal m of R and consider the extension Pm of P to R_m[t] (the localization at R-m). Because (Pm)_g is a free (R_m[t])_g module it follows from Horrocks result that Pm is a free R_m[t]-module and extended from R_m. Whence the Quillen-ideal for P equals R. Serre's conjecture follows by considering 1 and induction.