A multi-reflection time-of-flight mass spectrograph, competitive with Penning trap mass spectrometers, has been built at RIKEN. We have performed a first online mass measurement, using 8Li+ (T1/2 = 838 ms). A new analysis method has been realized, with which, using only 12C+ references, the mass excess of 8Li was accurately determined to be 20947.6(15)(34) keV (dm/m = 6.6 x 10-7). The speed, precision and accuracy of this first online measurement exemplifies the potential for using this new type of mass spectrograph for precision measurements of short-lived nuclei.