In a game in which both sides finished with 10 men, Albert upset the applecart by sending high-flying Berwick tumbling to defeat.
The only goal of the match came in the first half. A clearance from Rangers keeper Lyle Sloan rebounded off incoming Teri striker Peter Keenan and the ball spun loose to Michael McKenzie who netted from close range.
Both outfits had chances after this, but there was no addition to the scoring.
In the second period Albert’s Andy Williamson and Berwick’s Steven Bennett were both red-carded following an off-the-ball incident.
Hawick manager Graeme Chadwick said of his side’s showing: “I am delighted with the result.
“The guys did exactly what was asked of them and were superb.
“Every one of them gave me everything that they had. The attitude and commitment from every player was just brilliant and there is a real desire amongst the squad to do well this season.”