We report on experimental evidence of universality in ultracold 7Li atoms' three-body recombination loss in the vicinity of a Feshbach resonance. We observe a recombination minimum and an Efimov resonance in regions of positive and negative scattering lengths, respectively, which are connected through the pole of the Feshbach resonance. Both observed features lie deeply within the range of validity of the universal theory, and we find that the relations between their properties, i.e., widths and locations, are in excellent agreement with the theoretical predictions.