A single goal was enough to see the Millers extend their unbeaten run to ten league and cup games as they moved further up the table.
There was one change from the previous game with Paul Hurst coming into the line up as Ryan Taylor dropped down to the bench.
The home team had the first chance in the second minute when Craney sent Dsane through but Andy Warrington saved his shot.
The Millers replied with Dale Tonge having a shot saved before Mark Hudson delivered a fine cross to Steve Brogan who put his close range shot over the bar.
It was a scrappy opening period as the home team were quick on to the tackle in midfield but the Millers always looked the better team.
A good move saw a Hurst cross cut out before Chris O'Grady had a shot blocked and then a Brogan free kick was headed out. Hurst saw a shot dealt with in the same way before Pablo Mills joined the attack to have his shot saved.
Warrington did well to catch a home free kick but United were soon back on the attack again with Hurst having a shot saved and Graham Coughlan headed wide from a Brogan free kick.
At the other end Danny Harrison headed out a home corner before the Millers almost took a 37th minute lead when good work with Hurst and O'Grady saw the latter's shot deflected off Hudson for a goal kick.
Harrison was wide with a 20 yarder and from a similar distance Hudson was just off the target as the first half came to an end in stalemate.
At the start of the second period Ryan Taylor replaced Marc Newsham and there were early appeals for a penalty as O'Grady seemed to be held back but no whistle came.
Then on 52 minutes the Miller4s grabbed the lead with Brogan crossing to the far post when Hudson timed his run perfectly to knock the ball home.
It was almost two a minute later when O'Grady crossed but Hudson's shot this time was cleared off the line. For Stanley Craney fired wide but back came United again for O'Grady to have a shot blocked and another saved before it was almost two up on 60 minutes with a superb run from Taylor ending with a shot that went just wide.
Taylor then headed just off the target before Stanley at last pushed forward in search of an equaliser and Coughlan had to head out a corner following a free kick.
Tonge cleared well from McGivern and a home corner was well caught by Warrington before the Millers had yet another chance to wrap up matters on 75 minutes.
It came from another sweeping move involving Brogan and Hudson but O'Grady's shot was touché don to the post and cleared. Warrington had to produce a brilliant save on 81 minutes to keep out a shot from Craney and two home corners in quick succession were dealt with efficiently.
On 89 minutes Whalley had a good chance to level matters but all to could win was a corner that was cleared and almost five minutes of added time saw the Millers hold out for another valuable three points.
Accrington: Dunbavin, Cavanagh, Williams, Roberts, Procter, Harris, Edwards, Craney, Boco (Whalley 76), Dsane (McGivern 61), Mullin (McEvilly 88). Subs: Brown, Branch.
Rotherham: Warrington, Tonge (Joseph 82), Sharps, Coughlan, Hurst, Harrison, Mills, Hudson, brogan, Newsham (Taylor 46), O'Grady. Subs: Annerson, Yates, P. Holmes.
Referee: Mike Pike (Cumbria).
Attendance: 1,918.
