Flying insects perform aerial maneuvers through slight manipulations of their wing motions. Because such manipulations in wing kinematics are subtle, a reliable method is needed to properly discern consistent kinematic strategies used by the insect from inconsistent variations and measurement error. Here, we introduce a novel automated method that accurately extracts full, 3D body and wing kinematics from high-resolution films of free-flying insects. This method combines visual hull reconstruction, principal components analysis, and geometric information about the insect to recover time series data of positions and orientations. The technique has small, well-characterized errors of under 3 pixels for positions and 5 deg. for orientations. To show its utility, we apply this motion tracking to the flight of fruit flies, Drosophila melanogaster. We find that fruit flies generate sideways forces during some maneuvers and that strong lateral acceleration is associated with differences between the left and right wing angles of attack. Remarkably, this asymmetry can be induced by simply altering the relative timing of flips between the right and left wings, and we observe that fruit flies employ timing differences as high as 10% of a wing beat period while accelerating sideways at 40% g.