A goal in each half from Reece Burke and Devante Cole helped to secure a 2-1 win over Oldham, who had previously been unbeaten in Sky Bet League 1 this season before the game.
Oldham, who had Jonathan Forte sent off midway through the first half for a head-butt on Stephen Darby, pulled a goal back late on through defender Joe Mills but Parkinson's men comfortably, and deservedly, hung on for the three points.
A delighted Parkinson said: "We were out of the traps quickly, pinned Oldham back, and apart from a couple of sloppy moments, I felt we controlled the game for the most part.
"We got the goal in the first half, probably should have added a second before the break, so getting that second goal through Devante after the restart was important.
"The only real negative from the day was conceding the goal towards the end.
"All in all though, we are starting to look like a team who can sustain a performance across the course of the ninety minutes.
"Our mental strength and our physical strength is getting better, and it needs to keep improving."