Rafael Furcal drove in three runs and Javy Lopez added a solo homer for the Braves.
Furcal snapped a 3-3 tie by driving in a run with a single against Javier Vazquez (8-7) with the bases loaded in the sixth. Giles followed with his second career grand slam and Atlanta's fifth of the season.
Mike Hampton (7-5) allowed five runs and eight hits in six innings before being ejected in the top of the seventh for arguing after being called out for running inside the first base line.
Vladimir Guerrero homered twice, in the fourth and sixth inning, to give him 220 as an Expo. That moved him into a second-place tie with Gary Carter on the franchise list.