Animals use their olfactory systems to avoid predators, forage for food, and identify mates. Olfactory systems detect and distinguish odors by responding to the concentration, temporal dynamics, and identities of odorant molecules. Studying the temporal neural processing of odors carried in air has been difficult because of the inherent challenge in precisely controlling odorized airflows over time. Odorized airflows interact with surfaces and other air currents, leading to a complex transformation from the odorized airflow that is desired to the olfactory stimulus that is delivered. Here, we present a method that achieves precise and automated control of the amplitude, baseline, and temporal structure of olfactory stimuli. We use this technique to analyze the temporal processing of olfactory stimuli in the early olfactory circuits and navigational behavior of larval Drosophila. Precise odor control and calcium measurements in the axon terminal of an Olfactory Receptor Neuron (ORN-Or42b) revealed dynamic adaptation properties: as in vertebrate photoreceptor neurons, Or42b-ORNs display simultaneous gain-suppression and speedup of their neural response. Furthermore, we found that ORN sensitivity to changes in odor concentration decreases with odor background, but the sensitivity to odor contrast is invariant -- this causes odor-evoked ORN activity to follow the Weber-Fechner Law. Using precise olfactory stimulus control with freely-moving animals, we uncovered correlations between the temporal dynamics of larval navigation motor programs and the neural response dynamics of second-order olfactory neurons. The correspondence between neural and behavioral dynamics highlights the potential of precise odor temporal dynamics control in dissecting the sensorimotor circuits for olfactory behaviors.