The Robins exploited their total first-half dominance to record a first victory in four games.
Swindon could have taken an early lead, only for Matt Ritchie to sky over the bar from De Vita's cross.
But the pair combined to score after 28 minutes as Ritchie's cross ricocheted to De Vita, who fired low past the Alex Cisak from 10 yards.
Three minutes later Swindon doubled their advantage, with Nathan Thompson's ball in from the right finding De Vita for a 12-yard shot which took a heavy deflection and spun into the bottom corner.
Joe Devera's header almost made it three at the end of a first half in which Oldham failed to register an attempt on goal.
The home side improved after the break, but they went down to 10 men on 79 minutes when Cisak was forced off with a head injury - with all three substitutions already made, striker Robbie Simpson took over in goal.
Oldham's best effort came from Matt Derbyshire, whose shot was comfortably saved by Wes Foderingham.