The unprecedented extent of coverage provided by Kepler observations recently revealed outbursts in two hydrogen-atmosphere pulsating white dwarfs (DAVs) that cause hours-long increases in the overall mean flux of up to 14%. We have identified two new outbursting pulsating white dwarfs in K2, bringing the total number of known outbursting white dwarfs to four. EPIC 211629697, with T_eff = 10,780 +/- 140 K and log(g) = 7.94 +/- 0.08, shows outbursts recurring on average every 5.0 d, increasing the overall flux by up to 15%. EPIC 229227292, with T_eff = 11,190 +/- 170 K and log(g) = 8.02 +/- 0.05, has outbursts that recur roughly every 2.4 d with amplitudes up to 9%. We establish that only the coolest pulsating white dwarfs within a small temperature range near the cool, red edge of the DAV instability strip exhibit these outbursts.