Lee Brown's penalty three minutes before the break set Rovers on the way to victory before Rotherham debutant Claude Davis received his marching orders for his second yellow card in first-half added time.
Substitute Ellis Harrison doubled Bristol's advantage in the 53rd minute following a great solo run, and eight minutes later Joe Anyinsah broke down the right and made it three.
Substitute David Noble gave Rotherham back a little pride in the 73rd minute but that failed to dampen a fantastic afternoon for Ward.
"It's good to be off the bottom but we want to be better than that so it doesn't stop there," he said. "That's the first stage. We are trying to move a bit further if we can do that.
"We've had a nice little run, we've had five games and lost only one of them and we are still at the bottom because other teams have done well but it's nice now that there is a bit of movement to get above one or two of them.
"They came at us really strongly in the first 20 minutes and we had to get through that without a dent in it and we did that pretty well.
"Then we thought the game would settle into a pattern but then the goal and sending off changed it. We made the decision to keep the same shape because it was hard to break them down, then we scored two super goals with a bit of quality and we were able to find and use that bit of space that they lost with their man going off."
- Sports & Recreation
- Joe Anyinsah