This paper proposes a novel machine learning-enabled framework to robustly monitor the instantaneous heart rate (IHR) from wrist-electrocardiography (ECG) signals continuously and heavily corrupted by random motion artifacts in wearable applications. The framework includes two stages, i.e. heartbeat identification and refinement, respectively. In the first stage, an adaptive threshold-based auto-segmentation approach is proposed to select out heartbeat candidates, including the real heartbeats and large amounts of motion-artifact-induced interferential spikes. Then twenty-six features are extracted for each candidate in time, spatial, frequency and statistical domains, and evaluated by a spare support vector machine (SVM) to select out ten critical features which can effectively reveal residual heartbeat information. Afterwards, an SVM model, created on the training data using the selected feature set, is applied to find high confident heartbeats from a large number of candidates in the testing data. In the second stage, the SVM classification results are further refined by two steps: (1) a rule-based classifier with two attributes named 'continuity check' and 'locality check' for outlier (false positives) removal, and (2) a heartbeat interpolation strategy for missing-heartbeat (false negatives) recovery. The framework is evaluated on a wrist-ECG dataset acquired by a semi-customized platform and also a public dataset. When the signal-to-noise ratio is as low as -7 dB, the mean absolute error of the estimated IHR is 1.4 beats per minute (BPM) and the root mean square error is 6.5 BPM. The proposed framework greatly outperforms well-established approaches, demonstrating that it can effectively identify the heartbeats from ECG signals continuously corrupted by intense motion artifacts and robustly estimate the IHR. This study is expected to contribute to robust long-term wearable IHR monitoring for pervasive heart health and fitness management.