Via the world-line instanton method, we study electron-positron pair creation by a strong (but sub-critical) electric field of the profile E/ cosh 2 (kx) superimposed by a weaker pulse E / cosh 2 (ωt). If the temporal Keldysh parameter γ ω = mω/(qE) exceeds a threshold value γ crit ω which depends on the spatial Keldysh parameter γ k = mk/(qE), we find a drastic enhancement of the pair creation probability -reporting on what we believe to be the first analytic non-perturbative result for the interplay between temporal and spatial field dependences E(t, x) in the Sauter-Schwinger effect. Finally, we speculate whether an analogous effect (drastic enhancement of tunneling probability) could occur in other scenarios such as stimulated nuclear decay, for example.