The two promotion rivals were locked at one apiece with 16 minutes remaining when Northampton won a wide free-kick out on the right.
Two players would usually stand over the ball but on this occasion Pinnock moved away and drifted into the box whilst Sam Hoskins prepared to take the free-kick.
Hoskins' low ball into the area evaded all defenders and took a faint touch of Pinnock - according to the man himself - before going into the net via the post.
"I'm claiming it, 100 per cent! I know Sky haven't given me the goal but I think they have something in for me," said Pinnock.
"But Hosk put a great ball into the box and I definitely got a touch on it.
"We normally have two players out on those set-pieces but they were so open defensively so I said to him to put it into that front post area and fortunately enough I got across the front and got a touch.
"We needed it because the conditions were really tough, in the second-half especially the wind picked up so we couldn't clear the ball and it kept coming straight back on us."
That goal was enough for Cobblers to become the first away team to win at Exeter in nine months and 19 games.
"It feels like a big three points," admitted Pinnock. "I didn't actually know they hadn't lost at home for so long but we went into it like any other game.
"We know they're a good side but I felt in the first-half we were really strong.
"The second-half was difficult and we started slowly and they got the goal, but we showed good character to fight back and go and get the win and we were all buzzing in the changing room."
Pinnock played a more central role against Exeter as Town tweaked their shape.
"I had a bit of a different role," he added. "We set up as if to play five at the back with me and Rosey up front.
"We always had the option that, if they played as a four, we could have changed our shape and play what we normally play.
"But I actually enjoyed playing up front with Rosey. He gave me a chance in the first-half and we linked up quite well."