Midfield veteran Hardie's 65th-minute volley proved the difference between the sides as experience triumphed over youth.
It was the Ton's first win in three games and their opening success of 2013, and Moore had no doubt about how important the victory could prove.
He said: "Martin had been out with a thigh injury and has only managed light training, but he has come back and proved that experience and know-how are vital in these games.
"He has always had the ability to be in where it matters and he did it again for us. He has paid me back big time for the faith put in him.
"Now we have Livingston coming to us next and it is vital that we build on this victory."
For his part, 36 year-old midfielder Hardie was delighted with the 105th goal of his career.
Hardie said: "Experience is vital in these situations. That's 105 goals in my career and you don't lose the knack of knowing where to be for a finish.
"Falkirk have gone with youth whereas ourselves have retained experience and at the end of the day that worked for us."