Scrape off the rust around the leak. Use a hand wire brush or a rotary brush wheel on a power drill. Take your time to remove all layers of rust. Proper adherence of patching compounds requires a completely rustfree surface.
Paint the area to be repaired with a thin layer of black asphaltum paint. Allow the asphaltum to dry.
Cover the dried asphaltum with a 1/8-inch thick layer of plastic cement specifically designed for roof and gutter repair. Ordinary roofing cement may be substituted if this product is unavailable.
Cover the repair area with strips of heavy-grade aluminum foil while the cement is still wet. Where strips of foil meet, overlap the strips in the direction of water flow toward the downspout. Using a dry cloth, press the foil strips down into the cement; ensure the edges of the foil strips are well-cemented. Wear gloves to protect your hands from the cement.
Allow the repair to dry for at least one day. Use a garden hose to test for leaks.