We describe the operation and performance of the difference imaging pipeline (DiffImg) used to detect transients in deep images from the Dark Energy Survey Supernova program (DES-SN) in its first observing season from 2013 August through 2014 February. DES-SN is a search for transients in which ten 3 deg2 fields are repeatedly observed in the g, r, i, z passbands with a cadence of about 1 week. The observing strategy has been optimized to measure high-quality light curves and redshifts for thousands of Type Ia supernovae (SNe Ia) with the goal of measuring dark energy parameters. The essential DiffImg functions are to align each search image to a deep reference image, do a pixel-by-pixel subtraction, and then examine the subtracted image for significant positive detections of point-source objects. The vast majority of detections are subtraction artifacts, but after selection requirements and image filtering with an automated scanning program, there are ~130 detections per deg2 per observation in each band, of which only ~25% are artifacts. Of the ~7500 transients discovered by DES-SN in its first observing season, each requiring a detection on at least two separate nights, Monte Carlo (MC) simulations predict that 27% are expected to be SNe Ia or core-collapse SNe. Another ~30% of the transients are artifacts in which a small number of observations satisfy the selection criteria for a single-epoch detection. Spectroscopic analysis shows that most of the remaining transients are AGNs and variable stars. Fake SNe Ia are overlaid onto the images to rigorously evaluate detection efficiencies and to understand the DiffImg performance. The DiffImg efficiency measured with fake SNe agrees well with expectations from a MC simulation that uses analytical calculations of the fluxes and their uncertainties. In our 8 "shallow" fields with single-epoch 50% completeness depth ~23.5, the SN Ia efficiency falls to 1/2 at redshift z ≈ 0.7; in our 2 "deep" fields with mag-depth ~24.5, the efficiency falls to 1/2 at z ≈ 1.1. A remaining performance issue is that the measured fluxes have additional scatter (beyond Poisson fluctuations) that increases with the host galaxy surface brightness at the transient location. This bright-galaxy issue has minimal impact on the SNe Ia program, but it may lower the efficiency for finding fainter transients on bright galaxies.