The Welsh club ended a month-long winless run after overcoming Exeter last week.
And two goals in seven minutes through Ismail Yakubu and Danny Crow were enough for them to get back to winning ways at Rodney Parade.
Edinburgh said: "The most important thing was the result. We haven't won here in two home games so we had to see it through.
"Every game you play in this league you have to be resilient, sustain pressure, but I'm really pleased.
"It was a very good team display. They finished the game with five recognised strikers on the pitch and went for it. But credit to us we saw it out.
"The players showed great resilience and deserved the result."
Edinburgh left top scorer Chris Zebroski on the bench and was impressed by Crow as the striker took his chance.
The Exiles boss added: "When you're a manager you see the day-to-day training and attitude and sometimes a player twists your arm. He deserved his chance and showed why with the goal."
Yakubu handed the hosts the lead after nodding in Robbie Willmott's free-kick.
Within seven minutes they landed a colossal blow. Again Willmott provided the opening, and Conor Washington played in Crow, who expertly finished with his left foot.
Ade Azeez hit back within four minutes of coming on for Torquay, who continued to press but were unable to get the breakthrough as County hung on.