Pools won their previous three away games, but earned only their second home win thanks to a fine Luke James effort, despite being reduced to 10 men in the 25th minute.
Jack Compton was sent off but Pools were still too good for a Plymouth side who have now gone seven without a win.
"I have to say it's the most satisfying win," reflected Cooper. "You go away from home, look solid and express yourselves and win well. We have created chances and scored goals in those games.
"I wasn't happy with how we started, then we had a man sent off, but we became a team. That's how we had to get a result.
"Every player has given his heart and soul to Hartlepool United to make us win this game.
"I was proud, my emotions took over. The crowd got behind the lads to help them across the line.
"When they have come off the pitch I can still hear outside - I told them the crowd was right with them and fully behind them. Now they have to take it, don't get this support and then all flat.
"There's been a shift. We had a productive week, this was a grinder. As a former defender to see my team grind it out makes me very proud."