Urban functional zones are basic units of urban planning and resource allocation, and contribute to a wide range of urban studies and investigations. Existing studies on functional-zone mapping with very-high-resolution (VHR) satellite images focused much on feature representations and classification techniques, but ignored zone sampling which however was fundamental to automatic zone classifications. Functional-zone sampling is much complicated and can hardly be resolved by classical sampling methods, as functional zones are complex urban scenes which consist of heterogeneous land covers and have highly abstract categories. To resolve the issue, this study presents a novel sampling paradigm, i.e., heuristic sample learning (HSL). It first proposes a sparse topic model to select representative functional zones, then uses deep forest to select confusing zones, and finally embraces Chinese restaurant process to label these selected zones. The presented method collects both representative and confusing zone samples and identifies their categories accurately, which makes the functional-zone classification process robust and the classification results accurate. Experiments conducted in Beijing indicate that HSL is effective and efficient for functional-zone sampling and classifications. Compared to traditional manual sampling, HSL reduces the time cost by 55% and improves the classification accuracy by 11.3% on average; furthermore, HSL can reduce the variation in sampling and classification results caused by different proficiency of operators. Accordingly, HSL significantly contributes to functional-zone mapping and plays an important role in urban studies.