A Michael Collins strike proved decisive at the Withdean Stadium, as the Terriers backed up their 2-1 success at Leeds United with another victory.
Murphy has been in charge of the Terriers since Stan Ternent left the club earlier this month, and the improvement in form will aid his chances of getting the job on a permanent basis.
"The result showed the other side of our game. There was a lot of commitment and character, we really dug in and ground it out," he said.
"It was one of those games - the ugly side of football. Last week we played some very good football on a big open pitch, when Leeds came out and played football, but today that wasn't the case.
"I believe in the quality we have at this club and I cannot see a reason why we cannot continue on this run."