The home side put their defeat against England last week behind them to take a 34-10 win at Murrayfield.
The scrum-half told BBC Sport: "There have been tough times for fans, this one's for them.
"We had to do the dirty work. I'm fortunate enough to pick up the man-of-the-match but that's because the forwards did their job."
Scotland's interim coach Scott Johnson added: "I liked our intent. I think straight from the start we were aggressive. We had our chances and we scored off them."
Scotland's next Six Nations match is against Ireland in two weeks.