Moore, whose second coming as manager was announced on Thursday, was paraded to the crowd before kick-off and watched from the stands as his side broke the deadlock in the fifth minute.
Adam Le Fondre sprang the offside trap, rolled the ball across the six yard box and Kevin Ellison fired home.
Barnet came back with good efforts from Mark Hughes and Albert Jarrett before Rotherham doubled their advantage after 25 minutes with Nicky Law's first goal for the club.
Law timed his run to perfection to meet Tom Pope's pass and calmly lobbed the ball over the advancing Jake Cole.
On the hour, Le Fondre made it three with his seventh of the season after he raced on to Danny Harrison's pass.