Stewart Drummond's header gave the hosts the lead and although Barnet levelled through Matt Lockwood's penalty, Mark Duffy grabbed a deserved winner with 12 minutes remaining.
Lillis said: "It was a fantastic victory and I thought the lads showed outstanding character after being without a game for such a long time.
"We started superbly with a goal after just four minutes but I think we then thought it was going to be easy.
"It was great to get the new year off to such a great start after a frustrating few weeks for everyone. It keeps the pressure on the sides around the play-off zone and that is where we want to be."