Preheat oven to 325°. Stir together first 4 ingredients; gently stir in beer.
Place brisket, fat side up, in a large Dutch oven or roasting pan; pierce several times with a fork. Arrange potatoes and carrots evenly around brisket; then pour beer mixture evenly over brisket, potatoes, and carrots.
Bake, covered, at 325° for 3 1/2 hours, basting occasionally with sauce. Remove from oven, and let brisket stand in pan, uncovered, 20 minutes. Remove brisket from pan, and cut into slices. Return slices to pan with potatoes and carrots.