Metabolism fuels all biological activities, and thus understanding its variation is fundamentally important. Much of this variation is related to body size, which is commonly believed to follow a 3/4-power scaling law. However, during ontogeny, many kinds of animals and plants show marked shifts in metabolic scaling that deviate from 3/4-power scaling predicted by general models. Here, we show that in diverse aquatic invertebrates, ontogenetic shifts in the scaling of routine metabolic rate from near isometry (
b
R
= scaling exponent approx. 1) to negative allometry (
b
R
< 1), or the reverse, are associated with significant changes in body shape (indexed by
b
L
= the scaling exponent of the relationship between body mass and body length). The observed inverse correlations between
b
R
and
b
L
are predicted by metabolic scaling theory that emphasizes resource/waste fluxes across external body surfaces, but contradict theory that emphasizes resource transport through internal networks. Geometric estimates of the scaling of surface area (SA) with body mass (
b
A
) further show that ontogenetic shifts in
b
R
and
b
A
are positively correlated. These results support new metabolic scaling theory based on SA influences that may be applied to ontogenetic shifts in
b
R
shown by many kinds of animals and plants.