Loan pair Anton Forrester and Jordan Sinnott came in for their first starts and both scored in the first half, either side of a straight red card for Stanley striker Danny Webber.
Shakers substitute Marlon Jackson then netted late onto seal a first League Two win of the season for Blackwell's boys and leave the visitors still searching for their opening victory.
"It was our worst performance yet our best result," said Blackwell. "There was a bit of anxiety about the players and that was because they felt they deserved a result in the first couple of league games and it hasn't come.
"When the lads got the ball down and moved it quickly we looked decent and Danny Webber getting sent off opened up the game as well. It's always tough against 10 men but we went on to win 3-0.
"Jordan Sinnott grew as the game went on, there's no doubt he can see a pass, and Marlon Jackson came off the bench and took his goal with real style.
"It was the first time a lot of those players have played together so it's another game under our belt. We needed six to eight games in pre-season and we only had three. It is a learning curve with these players and I learned a bit more about them.
"I'm really pleased with their application and their attitude, and for me that result was a long time coming."