Two quick first-half goals helped Burton edge past bottom side Rotherham and move five points clear of the Championship relegation zone.
Burton gloveman Jon McLaughlin made several smart stops before Chris O'Grady tapped in against his old club to put the Brewers ahead.
The Millers had been on top but fell further behind when John Brayford crossed for Irvine to head home for a 2-0 lead.
It was Irvine's eighth goal of the season ensuring he sits way out in front as Burton's lead goal scorer, with his nearest rivals Jamie Ward and Lloyd Dyer both on four.
Tom Adeyemi reacted fastest to a save to pull one back, but Rotherham lacked the quality to find an equaliser.
Defeat leaves the Yorkshire side, led by caretaker-boss Paul Warne, 10 points from safety, while Burton move up two places to 19th.
It was a first away triumph of the season for Nigel Clough's side while O'Grady's goal was his first in 389 days, as he was on hand to score after Lewis Price spilled a shot.
Burton full-back Brayford spent several minutes being treated after a head injury, but came back on to assist Irvine before being replaced at the interval.
Rotherham were chasing back-to-back Championship wins for the first time this season, but they have now conceded 52 league goals.
Darnell Fisher volleyed wide and Izzy Brown could not find the target from inside the area as the hosts pressed, in vain, for a point.
Burton manager Clough was happy to end a brilliant 2016 with a first ever away win in the Championship.
"We didn't play anywhere near as well as we did at Aston Villa on Boxing Day but we battled away for three points," Clough said. "It was tough coming here, we knew that they would have their tails up.
"The only disappointment was that we conceded just before half-time and that gave them a chance, they put us under a lot of pressure in the second half.
"The timing in the year we didn't want to go into the new year without an away win and it was good to get that monkey off our back.
"We should have got a few more points than we have but it is important psychologically to not be in the bottom three going into the new year."
While Burton have reason to be hopeful it is the opposite for Rotherham, who are 10 points adrift of safety and look condemned to the drop.
It would have been different at New York Stadium had they converted a host of chances, but they only had Tom Adeyemi's effort to show for their dominance.
Caretaker manager Paul Warne said: "I thought we played really well, I thought that we were the better team and with respect to Burton I thought they came for a point.
"But there are so many chances you get in a game and if you don't take them you are snookered.
"Did they underachieve in the scoreline? Yes. But did they underachieve in the performance? No, I don't think they did.
"They are devastated, it will be tough to pick them up. But I don't believe we are relegated, I still think we have got a chance. If I didn't then I would tell the chairman to get a different caretaker in."