Brian Little's Welsh strugglers turned in a battling display after midfielder Matt Crowell had been red carded after just 13 minutes.
But Holmes sealed victory with two goals to take his tally to five in four matches after a six-week absence with a broken toe.
Young substitute Marc Newsham grabbed the third as the win revived Rotherham after their ten-match unbeaten league run had been ended in their last home match while Wrexham have now only won one of their last 12.
Wrexham might have grabbed an early lead when Chris Llewellyn raced clear down the right. His low cross caught out the home side but former Rotherham striker Michael Proctor was inches short of a scoring connection when he slid in.
Wrexham amazingly kept out the home side soon afterwards when a left-flank cross from Stephen Brogan was headed onto the bar by skipper Graham Coughlan.
Coughlan tried to stab in the rebound but the ball struck a defender and fell for Holmes but his hasty shot was straight at keeper Anthony Williams.
But the visitors were reduced to ten men after 13 minutes. Rotherham midfielder Ian Ross, making his debut after arriving on loan from Sheffield United, crashed to the ground when Crowell leapt in with a two-footed tackle and Surrey referee Gavin Ward gave him an instant red card.
Ten minutes before the break Rotherham found a way through. Ryan Taylor fed Brogan down the left and his cross reached Harrison. His shot was deflected into the path of Holmes and he struck a sweet shot home from ten yards out.
Rotherham should have stretched their advantage after 57 minutes when a slick move saw Chris O'Grady wide on the right and his cross found Ross. He controlled the ball but then hit a sloppy shot as Williams darted off his line and smothered the chance.
Dale Tonge hit another shot at WIlliams before and O'Grady found Marc Joseph in space but he curled his effort wide.
Wrexham created a chance on the break after 66 minutes as the pacy Sam Aiston tore forward, but Andy Warrington came off his line and blocked the ball with his body
Wrexham hung on until the 72nd minute when Ryan Taylor and Newsham linked well before Holmes slammed home a ten-yard shot.
And Newsham got in on the act when O'Grady set him up eight minutes from the end and the youngster provided an emphatic finish.