The tsunami source of the M_W8.1 2021 Raoul Island earthquake in the Kermadec subduction zone was estimated by inverting the tsunami signals recorded by DART bottom pressure sensors and coastal tide-gauges. The rupture propagated unilaterally northeastward from the hypocenter with maximum slip value of about 5 m, with features compatible with the aftershock distribution and rapid back-projection analysis. Three earthquakes of Mw ~8 or larger which also produced moderate tsunamis happened in the 20^th century in the same portion of the subduction zone. This is the first great tsunamigenic event captured by the new New Zealand DART network in the South West Pacific, which proved valuable to estimate a robust image of the tsunami source. We also show a first proof of concept of the capability of this network to reduce the uncertainty associated with tsunami forecasting and to increase lead time available for evacuation for future alerts.