Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of criticality uses automata network connectivity and node bias (to be on or off) as tuning parameters. This parsimony in the number of parameters needed sometimes leads to uncertain predictions about the dynamical regime of both random and systems biology models of biochemical regulation. We derive a more accurate theory of criticality by accounting for canalization, the existence of redundancy that buffers automata response to inputs -- a known mechanism that buffers the expression of traits, keeping them close to optimal states despite genetic and environmental perturbations. The new 'canalization theory' of criticality is based on a measure of effective connectivity. It contributes to resolving the problem of finding precise ways to design or control network models of biochemical regulation for desired dynamical behavior. Our analyses reveal that effective connectivity significantly improves the prediction of critical behavior in random automata network ensembles. We also show that the average effective connectivity of a large battery of systems biology models is much lower than the connectivity of their original interaction structure. This suggests that canalization has been selected to dynamically reduce and homogenize the seemingly heterogeneous connectivity of biochemical networks.