1. Dan Kan introduced Kan complexes and the Kan complex approximation functor $\mathrm{Ex}^\infty$ in the three-page 1956 PNAS paper "Abstract Homotopy III" (here is a JSTOR link). I can't resist pointing out his 1958 Trans. Amer. Math Soc. paper "Adjoint Functors"—clearly too long for this contest at 36 pages—where he defines an adjunction of functors on the first page. Here is a link.
2. The 1966 Quart. J. Math. Oxford paper $K$-theory and the Hopf invariant by Adams and Atiyah is only 8 pages long. I don't have a link to the paper, but here is a MathSciNet link. Adams and Atiyah use the Adams operations in $K$-theory to solve the Hopf invariant one problem. Adams' original proof (using secondary operations) takes 85 pages—of course that paper was extraordinarily fecund in homotopy theory.