Analytical solutions for steady, confined and unconfined Darcian flows in aquifers breached by "windows" in caprocks or bedrocks with applications to hillslope hydrology are presented. As compared with classical Polubarinova-Kochina, Numerov and Pavlovsky analytical solutions, the aquifers are sloping and the "window" is a finite-size isobaric segment, which due to the aquifer dip brings about a nonconstant head boundary condition. The velocity hodograph, method of boundary value problems and conformal mappings are used for obtaining solutions of essentially 2D seepage problems with Laplace's PDE as a governing equation and the nonlinear phreatic surface for an unconfined flow. The second-order hydraulic theory with Picard's iteration is used for deriving and solving a nonlinear ODE with respect to the shape of the water table, that is, compared with standard Dupuit-Forchheimer computations. The size of the "window," incident flow parameters upstream of the "window" and the angle of tilt determine the disturbance to a main aquifer, mundanely normal "longitudinal" flow, which may completely dive or unexpectedly extravasate into a commingled adjacent subjacent-superjacent layer.