The 23-year-old from Melbourne is now equal 7th in the top scorers race, having scored 33% of Burton's goals this season.
Irvine opened the scoring in the 15th minute, latching on to a lose ball just inside the box before slotting it past Rotherham's goalkeeper.
Irvine continues to impress since moving from Ross County in July this year.
Burton have been struggling for most of the season, but the win sees them three points clear of relegation.
Fellow Socceroos midfielder Tom Rogic was also on the score-sheet for Celtic, while Aaron Mooy completed 90 minutes for Huddersfield in a 1-1 draw.