Sammy McIlroy's team have found themselves near the foot of the table for most of this season.
But, although County have been struggling to find any form, they worked their socks off to snatch three vital points off the visiting Robins thanks to goals from Jim Goodwin and second-half substitute Chris Williams.
McIlroy was understandably overjoyed and he said: "It's the best I've felt for a while.
"We battled all the way and lads were magnificent.
"You have to set your stall out against second in the league - and that's what we did.
"It's very hard to be creative playing on our pitch, so we had to be more solid, and I felt we were more solid." Goodwin, making his first appearance since December, gave County the perfect start in the 11th minute.
The former Republic of Ireland Under-21 international replaced Fraser McLachlan in the Stockport's midfield and it did not take him long to make his mark.
A good cross from makeshift midfielder Danny Jackman was headed down by striker Aaron Wilbraham and Goodwin was there, just inside the penalty area, to fire the ball into the top right-hand corner.
Bristol, who are hoping for promotion this season, were left stunned to the core.
If it had not been for an excellent save from Steve Phillips, then the visitors might have gone further behind.
Danny Wilson's team did come close to levelling, both chances coming from free-kicks.
Bristol skipper Tom Doherty took the responsibility and was unlucky to see his 26th minute curler bounce to safety off the outside of the right post.
And, three minutes later, Doherty saw his quick free-kick saved comfortably by Williams at the near post.
However, Williams' arrival in the 88th minute sealed the points for McIlroy's team.
The youngster remained cool under pressure and lobbed Phillip with his first kick of the game.
Danny Wilson, the Bristol City manager, found time to joke about his side's shock defeat.
Wilson believed his team had the "lion share" of the chances and possession, but admitted Stockport had "deserved" their win.
"We're still second in the league - it's an absolute disaster," joked Wilson. "I'm not too disappointed because I felt we had the lion share of the game.
"I can't take anything away from Stockport, they battled hard and pressed us all day.
"But we are still in a great position and we must remain positive and keep going.
"We had enough chances to win the game and we hit the post twice. Unfortunately it didn't go our way."