Clough had seen his side fail to match their impressive home form on the road in recent weeks, but first-half goals from Jeff Hendrick and Craig Bryson ended the Rams' run of four consecutive away defeats.
A delighted Clough said: "We know that if we are to get where we want to be this season our away form has to improve, so this was a huge result.
"Bristol have been struggling at home, but they are still a dangerous side with some terrific away wins to prove that.
"We took our chances and then kept the ball well to kill off the game, so all credit to the players.
"Our aim remains as it was at the start of the season - to be a top-half team and see where that takes us.
"A clean sheet was a bonus because we haven't had too many of those and overall I'm very happy with the performance."