We prove ergodicity of conservative random dynamics satisfying a certain hyperbolicity condition. The new feature of our result is that we do not require the non-existence of zero Lyapunov exponents. As a particular application, we show that if \(R_1, R_2\) in \(\mathrm{SO}(d + 1), d ≥ 2\), generate a dense subgroup, then any pair \((f_1, f_2)\) of infinitely smooth volume preserving diffeomorphisms of the \(d\)-dimensional sphere that is sufficiently close to \((R_1, R_2)\) is ergodic with respect to the volume. Previously this was only known to hold when \(d\) is even by a result of Dolgopyat and Krikorian. Joint work in progress with Jonathan DeWitt and Dmitry Dolgopyat.