The Iron midfielder latched on to Freddie Sears' ball into the penalty area to despatch a clinical finish beyond Hull goalkeeper Matt Duke when the game appeared to be heading for a goalless draw.
The visitors bounced back from last week's 4-1 home defeat to Leeds with a spirited display in a typical derby encounter and have now won their last three away matches in the npower Championship.
Hull, who had their fair share of chances, are now without a win in their last seven league games and only goal difference prevented them from slipping into the bottom three.
Baraclough said: "After the 4-1 reverse against Leeds there was some criticism thrown at us and we've responded in the right way.
"I'm delighted by the clean sheet. Michael Raynes and Niall Canavan are two young defenders who were immense at the back. If they carry on like that they'll be our first-choice centre-backs at this club for years to come.
"But I thought everybody played their part in a good local derby. Our average age was 23, which is perhaps slightly too young for the championship, but everyone is chomping at the bit.
"Every away win is special and to come here to local neighbours and win is extra special. The fans can go back across the Humber and enjoy the weekend because we're the top dogs in this region at the moment.
"I asked them to play their natural game in the second half and we created chance after chance. If it hadn't been for (Hull goalkeeper) Matt Duke I think it could have been more.
"It was a great goal and if you were to see that on Match of the Day Alan Shearer would be crowing about it.
"If Michael O'Connor carries on like that (Northern Ireland manager) Nigel Worthington can't keep him out of the squad.
"The fans have always been great for me, they've backed me as a player, coach and now a manager. They shouted from start to finish and that's helped the players.
"The players realised that this was a critical game for the fans. It may not be as big as Everton-Liverpool or the Manchester derby but it means a great deal to our fans.
"We knew the Hull fans weren't happy and Nigel Pearson has a tough job on his hands. Given time and backing, Nigel Pearson will turn this club around."
Hull manager Nigel Pearson described the loss as "a poor result" and accepted a lack of goals is hurting his struggling side.
Pearson said: "We are clearly not scoring enough goals but we shouldn't have lost. Unfortunately for us we're not good enough at the moment. That's the reality.
"I can totally understand the reaction of the fans at the end and this result puts us all under a lot of pressure.
"I can't dress up the result - it's a poor result. This club was in the Premier League last year and many of the players here have Premier League experience.
"If you can't change the mentality of the players you have to change the players but I'm trying to rectify the situation with the tools I have.
"We have issues we need to rectify internally (such as the ongoing takeover situation) and until that happens things will not be easy. The sooner things are resolved, the better. There needs to be change at different levels of the club.
"I'd like to change a lot of things. We are in that (a relegation battle) already and our points return is poor. A result like that knocks the stuffing out of all of us. I think a draw may have been a fair result, but they had chances as well as us.
"We are in a bit of a corner and our Achilles heel all season has been goals."