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The Ne-18(alpha, p(0))Na-21 reaction provides one of the main HCNO-breakout routes into the rp process in x-ray bursts. The Ne-18(alpha, p(0))Na-21 reaction cross section has been determined for the first time in the Gamow energy region for peak temperatures T similar to 2 GK by measuring its time-reversal reaction Na-21(alpha, p(0))Ne-18 in inverse kinematics. The astrophysical rate for ground-state to ground-state transitions was found to be a factor of 2 lower than Hauser-Feshbach theoretical predictions. Our reduced rate will affect the physical conditions under which breakout from the HCNO cycles occurs via the Ne-18(alpha, p(0))Na-21 reaction.