Robinson pounced after 38 minutes when Terriers full-back Dean Heffernan swung in a cross which Oldham defender Reuben Hazell headed straight into the back of team-mate Dale Stephens and the ball fell kindly for Robinson, who produced a neat finish from close range.
And Huddersfield sealed the points in the third minute of stoppage time when Oldham were caught on the break and Gary Roberts squared for Robinson to notch his 13th goal from only 11 starts this season.
Victory for Lee Clark's side, in a game which Oldham dominated, consolidated their position in sixth spot and was their first home win in seven attempts.
Former Terriers striker Pawel Abbott hit the crossbar with a first-half header, while Lewis Guy and Hazell headed over in the first half.
Dean Furman set up Danny Whitaker for a 25-yard strike which flashed just wide of the post after 36 minutes. But any chance of an Oldham equaliser disappeared when Kieran Lee was sent off 14 minutes from time for a second yellow bookable offence.