Alex Sherzer, 18, of Fallston, Md., and Benjamin Finegold, 19, of Oak Park, Mich., shared first place in the U.S. Junior Invitational Chess Championship, which had its ninth and final round yesterday at the Ramada Renaissance Hotel downtown. Both players scored six out of a possible nine points. The 10-player tournament was hard-fought down to the last round, which opened with Sherzer leading the field by a point. Then he lost his final game to Vivek Rao of Monroeville, Pa., while Finegold defeated James Schuyler of New York. Third place was shared by Rao and Ilya Gurevich of Worcester, Mass., with 5 1/2 points each, and Stuart Rachels, the defending champion, finished fifth with five points. Sherzer will represent the United States in the World Junior Championship, which will be played in Colombia later this year, and Finegold will be seeded into the 1990 United States Invitational Championship. This was Finegold's last chance at the junior title, for which he will be overage next year, when co-champion Sherzer will still be eligible to defend his title. Gurevich, a master with a rating of 2570, was the highest-rated player in the tournament. Sherzer, rated at 2514, has fulfilled his requirements for an international master title, but it has not yet been formally awarded..