The TeX primitive \let allows you to identify control sequences. LaTeX counters are implemented by TeX count registers; the LaTeX command \newcounter{foo} creates a TeX counter \c@foo.
So you just need to make sure that the count registers for equation, section, and theorem are the same! LaTeX's \newtheorem command provides the functionality to make the theorem counter identical to the section counter. Use a \let to let the equation and section counters be the same.
\documentclass{article}
\newtheorem{thm}[section]{Theorem}
\makeatletter
\let\c@equation\c@section
\makeatother
\begin{document}
\section{First Section}
\begin{equation}
e = q^{uation}
\end{equation}
\begin{thm}
Ceci n'est pas une th\'eorem.
\end{thm}
\section{Second Section}
\end{document}
\numberwithin(GIYF) – kahen Jan 16 '12 at 20:39