Tranmere also finished with 10 men, although it was not until injury time that substitute Steve Davies also went with two yellow cards.
Barker had put Rotherham in front in the 14th minute with an excellent shot into the top corner following a Paul McLaren free-kick.
Tranmere's midfield star Danny Harrison was unlucky to hit a post in the 17th minute but the home side finally got level in first-half injury time with Chris Greenacre getting his 11th league goal of the campaign with an angled shot after his first effort was parried by Gary Montgomery.
Calvin Zola made it 2-1 on 54 minutes after United failed to clear a Simon Francis centre
Then Harrison made in 3-1 in the 61st minute with a good finish after Greenacre's centre had hit the bar.
But to their credit the Millers refused to lie down. They were unlucky not to get an own goal in the 75th minute when Gareth Roberts deflected the ball
But justice was done moments later as Tranmere keeper Dino Seremet turned aside a McLaren free-kick only for Will Hoskins to head in from the subsequent rebound.