Latics had won four of their previous five games, but they were comprehensively outplayed at Boundary Park.
Swindon had already missed a clear chance through Matt Ritchie when they scored in the 28th minute, Raffaele De Vita driving in Ritchie's cross from 10 yards.
De Vita struck again just three minutes later as he met Nathan Thompson's cross with a 12-yard shot which took a big deflection on its way past goalkeeper Alex Cisak.
Di Canio said: "In the first half we were excellent and we could have scored more than two goals. We dominated clearly and it's good to win because we have dominated other games and only taken one point.
"Oldham have very good, sharp players up front, but we defended well. We have Tranmere next and I'm happy that we will play the leaders. Before I was worried, now I'm happy.
"The fans can go home happy, not just with the goals and the points but also with the professional performance.
"Paolo Di Canio is insurance that players will be professional. I drive people crazy to do that, but it will always happen.
"Professionalism isn't wearing the tracksuit and carrying a cup of tea round the County Ground, it's 24-hour dedication and that's my mission.
"For sure, one day Paolo Di Canio will leave Swindon Town, but I want to have success and make the club bigger. You have to be mad not to love Paolo Di Canio."