I think a ton of papers by Paul Erdos fall under this category. (But interesting is in the eye of the beholder)
One I like is An Elementary Proof of a Theorem of Johnson and Lindenstrauss by Sanjoy Dasgupta and Anupam Gupta (Random Struct. Alg., 22: 60–65 (2003)) - it is about 5 pages long, but a lot of that is due to inane typesetting.
Abstract. -- A result of Johnson and Lindenstrauss shows that a set of $n$ points in high dimensional Euclidean space can be mapped into an $O(\log n/ϵ^2)$-dimensional Euclidean space such that the distance between any two points changes by only a factor of $(1 ± ϵ)$. In this note, we prove this theorem using elementary probabilistic techniques.
A lot of the earlier coding theory (and surprisingly a lot of papers in IEEE Trans. Info Theory and its predecessors up to the mid 70s, the original Huffman code paper for example) papers also fit this bill, such as the original Golay code paper.