Wireless local area network (WLAN) access points (APs) are being deployed in high density to improve coverage and throughput. The emerging multiple-input multiple-output (MIMO) implementation for uplink (UL) transmissions promises high per-user throughput and improved aggregate network throughput. However, the high throughput potential of dense UL-MIMO WLAN is impaired by multiple access channel interference and high contention among densely distributed user stations (STAs). We investigate the problem of actualizing the throughput potential of UL-MIMO in high density WLANs via user-AP association. Since user-AP association influences interference and STA contention, a method to optimally distribute STAs among APs is proposed to maximize aggregate users' throughput utility. This problem is transformed into a graph matching problem with the throughput utility function as the graph edge weights. The graph matching problem is solved as a combinatorial problem using a modified classical Kuhn-Munkres algorithm. A dynamic implementation of the proposed algorithm is used to periodically update user-AP associations when there are changes in the network due to new entrants and/or user mobility. Simulated dense UL-MIMO WLAN scenarios reveal that the proposed scheme achieves an average of $36.9 \%$, $33.5 \%$, $20.4 \%$ and $11.3 \%$ gains over the default strongest signal first (SSF) association scheme used in conventional WLAN, Greedy [14], SmartAssoc [13] and best performance first (BPF) [5] algorithms, respectively.