A sensitive probe of unconventional order is its response to a symmetry-breaking field. To probe the proposed p(x) +/- ip(y) topological superconducting state of Sr2RuO4, we have constructed an apparatus capable of applying both compressive and tensile strains of up to 0.23%. Strains applied along < 100 > crystallographic directions yield a strong, strain-symmetric increase in the superconducting transition temperature T-c. < 110 > strains give a much weaker, mostly antisymmetric response. As well as advancing the understanding of the superconductivity of Sr2RuO4, our technique has potential applicability to a wide range of problems in solid-state physics.