Hutchinson punished poor defending to head in on the stroke of half-time and although Derby had the majority of possession, they could not break down a disciplined Millwall side.
The Lions have now won 1-0 on their last three visits to Derby who remain seven points outside the relegation zone.
Derby ended a run of two defeats with a draw at play-off contenders Barnsley in midweek and they came the closest to scoring in the opening 15 minutes.
Both chances fell to full-back Forsyth who headed straight at Bartosz Bialkowski before he wasted an even better opening by glancing Nathan Byrne's cross wide at the back post.
Derby were dominating possession on a cold, blustery afternoon but Millwall, led by former Rams centre half Alex Pearce, were defending well and frustrated the home side who had created nothing after those Forsyth chances.
Millwall had hardly figured as an attacking force in a game short on quality and they again had to be alert when Martyn Waghorn whipped in a dangerous cross which Hutchinson cleared in the 40th minute.
Bialkowski palmed away a Kamil Jozwiak shot as Derby pressed but Millwall stunned them in the 45th minute by taking the lead against the run of play.
It was a poor goal to concede and left manager Wayne Rooney with a lot to ponder at half-time.
His side started the second on the front foot but the final ball lacked the quality to trouble a well-organised defence.
Millwall had kept Derby at arms length but they almost conceded in the 78th minute when Byrne's corner fell to substitute Sibley on the edge of the six-yard box but his shot came back off the bar.
It was the closest Derby had come and another sub, Patrick Roberts, had a shot charged down after he beat two defenders before Shinnie fired wide from outside the area.
Pearce made another vital interception after Roberts had made a good run and Millwall saw the game out to celebrate another three points at Pride Park.