Heart rate continuously varies due to autonomic regulation, stochasticity in pacemaking, and circadian rhythm, collectively termed heart rate variability (HRV), during normal physiological conditions. Low HRV is clinically associated with an elevated risk of cardiac arrhythmias. Alternans, a beat-to-beat alternation in action potential duration (APD) and/or intracellular calcium (Ca) transient, is a well-known risk factor associated with cardiac arrhythmias that is typically studied under conditions of a constant pacing rate, i.e., the absence of HRV. In this study, we investigate the effects of HRV on the interplay between APD, Ca, and electromechanical properties, employing a nonlinear discrete-time map model that governs APD and intracellular Ca cycling with a stochastic pacing period. We find that HRV can decrease variation in APD and peak Ca at fast pacing rates for which alternans is present. Further, increased HRV typically disrupts the alternating pattern for both APD and peak Ca and weakens the correlation between APD and peak Ca, thus decoupling Ca-mediated instabilities from repolarization alternation. We find that the efficacy of these effects is regulated by the sarcoplasmic reticulum Ca uptake rate. Overall, these results demonstrate that HRV disrupts arrhythmogenic alternans and suggests that HRV may be a significant factor in preventing life-threatening arrhythmias.