The Northern Blues, prior to this game, had gone over two games without a win in pre-season friendlies in Sudan and United Arab Emirates.
Midfielder Emmanuel Ocran opened the scoring in the first half, shifting the ball onto his left foot and rifling a thunderous effort into the top corner after Paul Asare De'veris' rebound.
The game marked the debut for Italian manager Vicenzo Annesse, who replaced Manuel Zacharias as Bechem's new head coach for the season.
Both sides were missing their top scorers from last season, but Bechem felt the absence more. Tetteh scored a hat-trick against All Stars a fortnight ago when his new club Al Hilal hammered the Ghana champions 3-1 in a friendly.
Annesse tried to rally his side in the second period, bringing several new signings, but it was skipper Badu Agyemang who had the best chance to level the score, only to blast the ball over the bar.
Coach Adipah lauded the qualities of Ocran and believes he will be the key to their success this season.
"Ocran is a wonderful player. We will count on him in the new season just like he delivered the cup to us against Bechem," Adipah told Goal.
"He was super in our run to win the league title and I am working on him to double his efforts.
"We will play a lot of games this time around because of the Caf Champions League and the introduction of the Ghana FA gala, so I will have to plan how to protect him.
Ghana Premier League will kick off on February 4, 2017 after litigation delayed the initial date.