The Millers, who were deducted 17 points by the Football League earlier this week, were on the attack early on at their new home as skipper Pablo Mills rifled inches wide with a long-range effort.
And Mark Robins’ side continued to press, with Danny Harrison’s shot being saved by Rob Burch while Mark Hudson shot narrowly over.
A minute before the break Reuben Reid snatched what proved to be the winning goal. The midfielder comfortably outpaced Lee Beevers in pursuit of a long ball from Mills and tucked his shot under the advancing Burch.
Rotherham could easily have doubled their lead two minutes after the break, but a great save from Burch denied Harrison.
At the other end, Lincoln’s best effort of a hard-fought second period was a free kick from Stefan Oakes which Andy Warrington tipped around the post.