Afterwards, Stanley boss John Coleman said it was a goal worthy of winning any game and certainly a candidate for the goal of the season.
"Our game plan was to stay in the game for as long as possible and then to pick them off on the break. It worked. That is just what we did," he said.
There was little quality from either team and the home side managed just one shot on target in the first period, and that was one more than Accrington, who seldom crossed the halfway line.
The game was littered with fouls and stoppages and there were early bookings for Rotherham's Joe Widdowson and Stanley's Phil Edwards.
The only shot on target in the entire first half came after 39 minutes from Rotherham's Ryan Taylor, but it was so weak that it was easy for Kenny Arthur in the Accrington goal.
In the swirling wind, both teams persisted in throwing high balls into the area but that just made it easy for the defences, where Darran Kempson had an impressive debut for Stanley following his loan signing from Shrewsbury Town.
The only moment of panic for Stanley's defence was brought about by themselves.
Mark Roberts tried to head back to his own keeper, but the ball looked to be heading for the corner of the net until Arthur scrambled across to turn the ball for a corner.
There was little or no improvement after the break with Rotherham continuing to do most of the pressing, but all that changed in the 64th minute when Stanley grabbed a shock lead.
Andrew Mangan and Paul Mullin launched a quick break down the right before the ball was picked up by Craney, who hit a magnificent 25-yard shot that surprised everyone and flew into the top corner.
From then on it was backs to the wall for Stanley as they fought to preserve their lead, but in truth Rotherham were simply not up to the task and the visitors had little difficulty holding on for victory as the only offering of a Millers goal came from Chris O'Grady's low effort.