Town were on the cusp of just their third away win of the campaign and first since October 1 going into the final stages at the New York Stadium with goals from Vaughan and Conor Coady giving them a deserved 2-0 lead against the Millers.
But the hosts produced a grandstand finale with goals in the 88th and 90th minutes from substitutes Jonson Clarke-Harris and Lee Frecklington securing an unlikely draw.
Prior to that, it had been a near-perfect away-day from Town, who had lost their previous four matches on the road and who went into the game on a worrying run of five defeats in their last seven outings.
Vaughan, handed a start alongside Grant Holt - who came off injured in the second half, making him a big doubt for Sunday’s Roses clash with visiting Bolton Wanderers at the John Smith’s Stadium - netted in the 35th minute to put Town ahead.
It was the striker’s first goal since November 30, 2013.
Coady’s header following a pinpoint cross from sub Gobern, who had earlier replaced Holt, doubled Town’s advantage in front of their 2,609 contingent in the sell-out crowd of 11,681 - but a stirring late really saved the day for the Millers, to the deflation of the visiting fans.
On the input of Vaughan and Gobern, Powell added: “James has been out for a long time and we have tried to build up his fitness and he has some substitute appearances and been training well.
“With the quick turnaround, I knew it was an opportunity to give him a start and I thought for seventy-plus minutes, he was a real thorn in the side of Rotherham and deserved his goal.
“Hopefully now, that’s him on his way. We will see how he recovers and whether he has enough in reserve to play against Bolton.
“But of course, we lost Grant Holt, so we don’t know how that is. We will just have to have a head-count like every other team and get ready for Bolton.”
On the contribution of Gobern, making his first appearance of the season for Town, Powell added: “We lost Jonathan Hogg through illness, normally over the Christmas and winter time, you usually get one or two and one or two staff members have got it as well.
“Oscar has been training well and on the fringes, but to be fair to him, he’s got on with it and earned the right to be in the 18 against Rotherham.
“He got an assist which will be good for him mentally and we will see where it goes from now for him.
“He does have a lot of qualities which are taylor-made and suited to the Championship. Hopefully he can play a part in the up and coming games.”