Irvine is now equal second in the Championship top goalscorers list along with, among others, cult-hero Will Grigg on four goals. Bristol City's Tammy Abraham, on loan from Chelsea, leads the pack on six goals.
The Australian midfielder took his tally to four when he placed a shot from the edge of the box into the bottom right-hand corner in the 51st minute to open the scoring.
However it was heartbreak for Burton as Fulham equalised in the 90th minute when Ryan Sessegnon pounced on a goalkeeping error by Jon McLaughlin.
Irvine, 23, continues to impress after joining Burton in July.
The draw means Burton moves up to 15th place, above Wolverhampton Wanderers and below Queens Park Rangers, while Fulham is in sixth.