Sensitive magnetoconductance measurements have been made on clean Al films and submicrometer-width wires. Theoretical expressions for the magnetoconductance (MC) provide a good fit to the data only after high-field corrections are made to the Maki-Larkin term. Analysis of the MC data is used to infer the temperature-dependent electron inelastic scattering rate 1/i in the vicinity of the superconducting transition temperature Tc. At temperatures just above Tc, the coupling between electrons and superconducting fluctuations is expected to affect significantly the inelastic scattering rate, producing a rapid rise in 1/i as T approaches Tc from above. We observe this novel behavior in both one- and two-dimensional samples and find it to be in good quantitative agreement with recent theoretical predictions.