Graham netted 12 top-flight goals for the Swans last term but his strike against the Cottagers was only his second Premier League goal of this campaign.
But he stepped up just at the right time in the absence of leading goalscorer Michu, who suffered an ankle injury in the previous goalless draw with Reading.
Laudrup told the Sunday Express: "It was great for Danny to score. It was very important for us but maybe more important for him.
"We had to find a solution with Michu not there, and Danny did a great job. He hasn't scored a lot this season but when a striker scores one, they can suddenly score four or five.
"You can't always win the same way. Sometimes you have to learn to use a Plan B or a Plan C. We showed great character."