We present the first large-acceptance measurement of event-wise mean transverse momentum < p(t)> fluctuations for Au-Au collisions at nucleon-nucleon center-of-momentum collision energy root s(NN) = 130 GeV. The observed nonstatistical < p(t)> fluctuations substantially exceed in magnitude fluctuations expected from the finite number of particles produced in a typical collision. The r.m.s. fractional width excess of the event-wise < p(t)> distribution is 13.7 +/- 0.1(stat) +/- 1.3(syst)% relative to a statistical reference, for the 15% most-central collisions and for charged hadrons within pse...