Stanley were propping up the League Two table last month but are now 20th and hold a three-point advantage over second-bottom Torquay.
A brace from Kal Naismith made it four wins in five league games for Stanley as they came from behind after Paul McCallum had given the Gulls a 14th-minute lead.
"I'm delighted for the players and for the fans," Beattie said. "Only a small percentage of teams come from behind to win games and we have done it twice this season.
"There was a lot of emotion in the dressing room at half-time as we had words although there wasn't a lot wrong with the performance.
"Torquay are a good, organised side and they caused us problems but we got ahead in the second half and then saw the game out.
"It's a great feeling to win and now we have got to concentrate, not get carried away and keep applying ourselves. I believe there is a lot more to come from this side."
- Sports & Recreation
- Kal Naismith
- Paul McCallum