Atfer an early strike by Adam Le Fondre, City had levelled after the break before Cresswell won the spoils for the home side with a firm close range header from Nicky Law's teasing cross in the 88th minute.
With half of Rotherham's side on the treatment table it seems, a new look back four lined up against old man Drewe Broughton and what promised to be a physical looking Lincoln outfit containing pace in wide areas.
The visitors had the first attempt on goal as two of their new boys combined, Josh O'Keefe heading an Albert Jarrett corner wide of Andy Warrington's upright.
But it wasn't long before hot shot Le Fondre picked up where he left off last season, firing the ball into the roof of the net clinically on 9 minutes after Kevin Ellison's effort at the far post was only half cleared off the line by the Imps defence.
In truth Rotherham bossed the first half with some neat interplay, Tom Elliott also looking strong upfront in support of Le Fondre.
Indeed it was Elliott, on loan from Leeds, that came the closest to adding a second before the interval, with two headed efforts, the second going narrowly wide of Joe Anyon's post after good play between himself and Law.
The second half saw City come out more positive and they drew level after 53 minutes when Dean Holden allowed Mustafa Carayol too much time on the left and his well struck cross shot flew past Warrington and a host of bodies into the bottom corner.
A sluggish home side were poor to react and almost conceded a second on the hour as Carayol jinked past several challenges before wasting his good work by blasting well over Warrington's crossbar.
Le Fondre almost gave the Millers the lead again on 71 minutes, but his header went over after Holden's run and right wing cross into the area.
But after good play centrally by substitute Mark Bradley with just two minutes to play, Law found space on the right, beat his marker and delivered his best ball of the game allowing delighted skipper Cresswell to do the rest.