The former England captain was officially confirmed as the Rams' manager on Friday, having held the post on an interim basis since the departure of Phillip Cocu in November.
But his reign got off to an inauspicious start as Lindsay's late strike sent County second bottom of the table.
Rotherham moved ahead of their opponents on goal difference and they also have two games in hand on the teams around them.
The standout news from Rooney's team selection was his decision to hand the captain's armband to 19-year-old Jason Knight.
Knight's midfield colleague Graeme Shinnie registered the game's first shot on target when he hit a rasping drive which visiting goalkeeper Jamal Blackman was more than equal to.
Rotherham then broke quickly, with Wes Harding picking out Michael Smith inside the area, but he could only plant an effort wide.
Lee Buchanan drilled an effort towards Blackman's right-hand post after 26 minutes, but the Chelsea loanee got down quickly to turn it behind for a corner.
Rotherham thought they had taken the lead 10 minutes before the break. Captain Richard Wood applied a fine finish inside the area but, after a brief delay, Wood was ruled offside and the goal was chalked off.
The second half was an even more cagey affair, with chances at a premium. Martyn Waghorn fluffed a rare opportunity when well-placed after 70 minutes, firing wide of goal from just a couple of yards out.
The game livened up as it headed into the latter stages and Shinnie again tested Blackman from close range before Waghorn's looping header almost caught the keeper off-guard.
But, after soaking up pressure, the Millers snatched victory against the run of play in the 86th minute.
Shortly after having a goalbound effort hacked away by a back-tracking defender, Lindsay knocked home the winner from a few yards after Daniel Barlaser's free-kick had crashed against a post.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click HERE to subscribe.