Thermostabilizing enzymes while retaining their activity and enantioselectivity for applied biocatalysis is an important topic in protein engineering. Rational and computational design strategies as well as directed evolution have been used successfully to thermostabilize enzymes. Herein, we describe an alternative mutability-landscape approach that identified three single mutations (R11Y, R11I and A33D) within the enzyme 4-oxalocrotonate tautomerase (4-OT), which has potential as a biocatalyst for pharmaceutical synthesis, that gave rise to significant increases in apparent melting temperature Tm (up to 20 °C) and in half-life at 80 °C (up to 111-fold). Introduction of these beneficial mutations in an enantioselective but thermolabile 4-OT variant (M45Y/F50A) afforded improved triple-mutant enzyme variants showing an up to 39 °C increase in Tm value, with no reduction in catalytic activity or enantioselectivity. This study illustrates the power of mutability-landscape-guided protein engineering for thermostabilizing enzymes.