Rotherham’s victory was set up by a promising first-half performance during which they scored two tries by forwards Alex Reider and Jack Preece.
Carnegie were punished further by second-half penalties by Rotherham’s Ulster fly-half James McKinney, who struck goals on 53 and 63 minutes.
Carnegie had the chance of scoring a try late in the second half but full-back David McIlwaine was robbed of the ball by Rotherham debutant winger Craig Dowsett, who made an impressive first appearance.
Carnegie’s only score came just before half-time as fly-half Christian Georgiou struck a penalty.After that Rotherham’s control was never seriously threatened.
Rotherham, with four players making their debuts, nearly scored after six minutes following a powerful break by centre Jack Roberts.
However, Carnegie, a mixture of Championship and academy players, cleared the danger. Carnegie’s McIlwaine then caused alarm in the Rotherham 22 with a threatening move, but the chance of a try collapsed as prop Hill lost possession.
Rotherham suffered a blow on 20 minutes when hooker and captain Tom Cruse withdrew because of injury.
They deservedly went ahead on 25 minutes as a result of excellent work by the pack who stole possession at a Carnegie lineout.
Titans’ flanker Reider crashed over in the corner and with flyhalf McKinney converting, Rotherham seized a 7-0 lead.
Five minutes later, Rotherham’s pack excelled again close to the Carnegie line as they increased the pressure.
From another successful lineout, replacement hooker Preece was driven over for his side’s second try and as McKinney put over his second conversion, Rotherham were in control at 14-0.
Just before half-time, Georgiou kicked a penalty, cutting Rotherham’s lead to 14-3.
Yorkshire Carnegie: McIlwaine, Prell, Vickerman, Fitzpatrick, Tai (Allen, 66), Georgiou, Dudman (Goss, 67), Beech (Boyce, 60), Hayes (Walker, 53), Hill (Hooper, 58), Edwards (Borrowdale, 67), Cassom, Barnard (Grange, 67), Walker, Williams.
Rotherham Titans: Scanlon, Broadley, Gill (J Davies, 54), Roberts, Dowsett, McKinney (Barrett, 64), A Davies (McGaffin, 65), Gadd (Williams, 54), Cruse (Preece, 20), Tampin (Macklin, 63), Harker, Robinson, Argyle, Reider, Morris (Birch, 20).
Referee: Jamie Leahy (RFU).