The floodlights failed with ten minutes left but City lit up their pre-season programme with this win at the Don Valley Stadium.
DJ Campbell did the damage again for City, his winner being his third in successive pre-season games.
The visitors were soon on the attack, Paul Gallagher chasing down a rather short pass-back but the keeper cleared.
After a Rotherham corner was wasted, City swept upfield through Nicky Adams and from the resultant cross, the ball was played back to Gallagher for a 20-yarder saved.
When Richie Wellens sent over a superb cross onto the head of DJ Campbell, the striker should have scored but headed wide as City looked to have the edge and sure enough they went ahead in the 12th minute when a cross from Lloyd Dyer was turned back to Gallagher who blasted home a fine finish.
It was no more than City deserved and soon after, in a sweeping move a right-wing cross was cleared, the heat staying on for Steve Howard to shoot just over.
But City's grip on the game was loosened in the 18th minute when Chris Weale, rushing out to clear a short pass-back from Tom Kennedy, flattened Tom Elliott on the edge of the area for a penalty well converted by Adam Le Fondre..
This gave the Millers a boost and Jack Hobbs had to clear when the visitors were almost caught out again. Later Michael Morrison lost possession to Elliott and the cross led to a shot by Le Fondre being well saved by Weale.
After a few more scares for City, they almost snatched back the lead in the closing stages of the half when Campbell was fouled inside the D and his own shot from the free-kick was deflected just wide.
City made eight changes for the second half, Kennedy, Hobbs and Campbell being the only ones left in the side and the new set-up almost came a cropper as, in the opening minutes of the half, an Elliott shot came back off the left-hand post with Logan diving full length but the visitors recovered.
Aman Verma sent Dany N'Guessan in on the right and his cross-shot was saved by the keeper. Next, Matty Fryatt went through into the area where he was barged to the ground but no penalty wad forthcoming although it did show City's attacking intent.
After more good stuff from City, N'Guessan had a shot blocked and a fine 20-yarder from Fryatt needed a good save.
The pressure told on the hour mark when, after a fine move, Campbell made room to score with a clinical finish for what proved to be the winner.
But the home side were still battling and when a Le Fondre cross from the left found Danny Harrison in the clear, the equaliser looked certain but the striker blasted high and wide from close range.
City could have stretched their lead when a fine run by N'Guessan ended with a fierce shot blocked, the same fate suffered by Yann Kermorgant's follow-up.
Later, Logan saved from Le Fondre but any chance of a fightback were ended with ten minutes left when the floodlights failed, causing the end of the action..
City: Weale; Adams, Morrison, Hobbs, Kennedy, Gallagher, King, Wellens, Dyer, Howard, Campbell. Subs: Logan(46 for Weale), Fryatt (46 for Howard), Oakley (46 for King), Parkes (46 for Morrison), Neilson (46 for Adams), N'Guessan (46 for Gallagher), Kermorgant (46 for Dyer), John (75 for Kennedy), Verma (46 for Wellens), Schlupp (65 for Campbell).
Rotherham: Warrington; Green, Cresswell, Fenton, Newey, Law, Taylor, Bradley, Ellison, Elliott, Le Fondre. Subs: Harrison (46 for Bradley), Brogan (73 for Newey), Ashworth (75 for Fenton), Warne (60 for Laws), Marshall (60 for Ellison), Darley, Annerson.
Referee: C Pawson.
Attendance: 1,131.
