The Lavochkin was the only Soviet fighter to shoot down a German jet, with La-7 ace Ivan Nikitovich Kozhedub fighting and downing one Me 262 jet on February 15, 1945 over eastern Germany. Kozhedub apparently later said that his success was mainly due to the Me 262 pilot attempting to out-turn his more maneuverable plane.
http://en.wikipedia.org/wiki/Messerschmitt_Me_262