Tony McMahon's fourth goal of the season early into the second period was enough to secure the victory for Parkinson's men against an Oldham side buoyed by the recent arrival of new manager John Sheridan.
The game - City's first home league match in 53 days - also saw Oldham substitute defender Connor Brown given a straight red card shortly before the interval for a fierce challenge on Kyel Reid.
Parkinson said: "I was very pleased with the lads' efforts today (Saturday).
"It was always going to be a tough game with it being John's (Sheridan) first game in charge of Oldham.
"Oldham have also done reasonably well away from home this season as well so we knew the match would be a challenge.
"We got into some fantastic positions in the first half but we know that our final ball probably wasn't the best.
"We got the goal in the second half though, and we were strong and resolute around the pitch and deserved the win.
"Starting from the Coventry game really, our last league game at home, Tony (McMahon) has kept getting into those scoring positions.
"He's got a good connection with the header and it has looped back across goal and into the corner.
"After losing a couple of away games in the league, it was very important that we got back to winning ways.
"This win is a huge boost for us."