Giovinco knuckled it just inside the left post from 35 yards out for his fourth goal of the season.
Toronto FC (3-4-0) opened the season away from home to allow for renovations of its BMO Field. TFC had a four-game losing streak after winning the season opener but rebounded to win the last two.
Chris Konopka earned his first MLS shutout while making his first start for Toronto.
Cristian Maidana had the Union's best chance in first-half stoppage time when he crashed a left-footed shot into the crossbar. The Union (1-6-3) lost their third straight and extended their winless streak to four.