Galhardo scored with a penalty 10 minutes before half time to add to an earlier strike by Edenilson.
It was his 14th goal of the Brazilian league season and takes Inter to 34 points, level at the top with Flamengo, who hammered Corinthians 5-1 earlier in the day.
Atletico Mineiro have 31 points but have two games in hand.
Vasco’s loss was their eighth game without a win and leaves them in 13th position in the 20-team table. (Reporting by Andrew Downie in London; Editing by Muralikumar Anantharaman)