Counterintuitive order-disorder phenomena emerging in antiferromagnetically coupled spin systems have been reported in various studies. Here we perform a systematic effective field theory analysis of two-dimensional bipartite quantum Heisenberg antiferromagnets subjected to either mutually aligned -- or mutually orthogonal -- magnetic and staggered fields. Remarkably, in the aligned configuration, the finite-temperature uniform magnetization $M_T$ grows as temperature rises. Even more intriguing, in the orthogonal configuration, $M_T$ first drops, goes through a minimum, and then increases as temperature rises. Unmasking the effect of the magnetic field, we furthermore demonstrate that the finite-temperature staggered magnetization $M^H_s$ and entropy density -- both exhibiting non-monotonic temperature dependence -- are correlated. Interestingly, in the orthogonal case, $M^H_s$ presents a maximum, whereas in mutually aligned magnetic and staggered fields, $M^H_s$ goes through a minimum. The different behavior can be traced back to the existence of an easy XY-plane that is induced by the magnetic field in the orthogonal configuration.
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