State-of-the-art petawatt laser beams may be focused down to few-micron spot sizes and can produce violent electron acceleration as a result of the extremely intense and asymmetric fields. Classical fifth-order calculations in the diffraction angle show that electrons, injected sideways into the tightly focused laser beam, get captured and gain energy in the GeV regime. We point out the most favorable points of injection away from the focus, along with an efficient means of extracting the energetic electron with a static magnetic field.