We report on the first demonstration of femtosecond x-ray absorption spectroscopy, made uniquely possible by the use of broadly tunable bending-magnet radiation from "laser-sliced" electron bunches within a synchrotron storage ring. We measure the femtosecond electronic rearrangements that occur during the photoinduced insulator-metal phase transition in VO2. Symmetry- and element-specific x-ray absorption from V2p and O1s core levels (near 500 eV) separately measures the filling dynamics of differently hybridized V3d-O2p electronic bands near the Fermi level.