The striker, who recently returned from a four-month injury lay-off, won the decisive free-kick with 13 minutes remaining after being tripped by Adrian Mariappa, and was then in the right place at the far post to head in Jon Hendrie's ball in.
Clough said: "It's been a long, long wait for it (a first away win). but for the three performances we've put in this week we've deserved to win at least one of those games.
"We could have easily beaten West Brom (drew 2-2), could have won at Preston (drew 0-0), but we got our victory here. The level of the three performances has been excellent.
"We look solid, we restricted an extremely good attacking side to very few opportunities and then we looked relatively dangerous ourselves, certainly compared to what we have done in the previous away games.
"We just felt if we kept it at 0-0, put the ball in the right areas then on a very difficult surface we might just get some reward today."
Watford went into the game looking for a fifth successive home win, and the match could have turned out differently had Danny Graham taken advantage of a scuffed clearance from Derby keeper Stephen Bywater, but his first-time attempt from 40 yards drifted narrowly wide.
Bywater then made a smart stop at the end of the opening period to deny Heidar Helguson.
Although the match improved after the break, scoring opportunities remained hard to come by, but Tom Cleverley's curling effort forced another fine save out of the Rams keeper with 20 minutes remaining.
But, after Porter had made the breakthrough, the home side should have equalised soon after when John Eustace found himself in a great position in the area but lifted the ball just over the angle of post and bar.
But Watford manager Malky Mackay had few complaints about the outcome.
He said: "Derby came here and deserved to go away with the three points because we weren't consistent enough in our decision-making and in the way we went about our job today.
"Usually the person on the ball makes the correct decisions in the main but I thought we had too many people today who were not making the right decisions when they had the ball in terms of what they were going to do with it."
Referee Keith Stroud booked seven players, including five for the home side, in a match of few chances.
Mackay said: "I know the referee has given out seven red cards in 12 games this season and I can see why.
"Some bookings I truly thought were strange decisions."