Graph matching (GM) aims at discovering node matching between graphs, by maximizing the node-and edgewise affinities between the matched elements. As an NP-hard problem, its challenge is further pronounced in the existence of outlier nodes in both graphs which is ubiquitous in practice, especially for vision problems. However, popular affinity-maximization-based paradigms often lack a principled scheme to suppress the false matching and resort to handcrafted thresholding to dismiss the outliers. This limitation is also inherited by the neural GM solvers though they have shown superior performance in the ideal no-outlier setting. In this paper, we propose to formulate the partial GM problem as the top-k selection task with a given/estimated number of inliers k. Specifically, we devise a differentiable top-k module that enables effective gradient descent over the optimal-transport layer, which can be readily plugged into SOTA deep GM pipelines including the quadratic matching network NGMv2 as well as the linear matching network GCAN. Meanwhile, the attention-fused aggregation layers are developed to estimate k to enable automatic outlier-robust matching in the wild. Last but not least, we remake and release a new benchmark called IMC-PT-SparseGM, originating from the IMC-PT stereomatching dataset. The new benchmark involves more scale-varying graphs and partial matching instances from the real world. Experiments show that our methods outperform other partial matching schemes on popular benchmarks.