The Miners made it two wins out of two games after handing the Phobians a 3-1 home defeat in Cape Coast.
James Akaminko, Amos Addai and Shafiu Mumuni ensured three points for the away side, with Hearts' consolation coming from Joseph Esso.
"Tactically we were better and more disciplined," Akonnor said.
"We knew exactly what we had to do to win this game and I think we did it well, we made them suffer to see the ball.
"I told the boys to keep the ball and they heeded to my instruction which made things difficult for Hearts of Oak.
"We fully deserved the three points because we were better on the day."
Ashgold consequently sit top of the league table with six points ahead of Sunday's round of matches.
The 2014-15 champions beat Wa All Stars 1-0 on matchday one.
Hearts, meanwhile, have just a point to their name as they drew with new boys Eleven Wonders on the opening day.