We apply the time-dependent theory of laser catalysis to the collinear exchange reaction A+BC --> AB+C. We have performed detailed calculations of pulsed laser catalysis on two-dimensional potential surfaces resembling the ground and first excited electronic potentials of the collinear H+H-2 reaction, at various incident energies and laser central frequencies. As in the one-dimensional case, the resulting reactive lineshapes are Fano-type curves, with tunneling enhancement on the blue side of the radiatively broadened line and suppression on the red side. Transmission coefficients range from zero to unity, depending upon the laser detuning. The points of complete transmission and complete reflection are explained by constructive and destructive interference between nonradiative tunneling and the optical path.