Clough, who has been given permission to hold talks with his former club Nottingham Forest about their managerial vacancy, saw goals from Luke Murphy and Lloyd Dyer put his side in control before Conor Washington pulled a goal back in this Championship clash.
Both Irvine and Luongo played full games for their respective teams, with both picking up late yellow cards as well for their troubles.
Murphy, on loan from Leeds United, sent a powerful low shot into the bottom corner of the net from 30 yards on 11 minutes.
It was his first goal for Burton and their first goal in five matches.
And worse followed for QPR six minutes into the second half, when Dyer finished coolly after exchanging passes with on-loan Fulham midfielder Lasse Vigen Christensen.
Washington, on as a half-time substitute, hauled QPR back into the game just after the hour mark.
The striker kept his composure after a sliding challenge from John Mousinho and smashed the ball past keeper Jon McLaughlin.
But Burton held on fairly comfortably to pick up only their second win in nine league league matches which takes them out of the relegation zone.
QPR boss Ian Holloway made two surprise changes to his starting line-up, with on-loan Brighton winger Kazenga LuaLua and Michael Doughty replacing Jamie Mackie and Ryan Manning. But they were behind after just 11 minutes thanks to Murphy's strike.
With his team having failed to create a clear-cut chance in the first half, Holloway brought on Washington and switched to two up front in an attempt to change the course of the game.
Instead, QPR switched off at the back and the lively Dyer took full advantage.
Washington eventually did have an impact - and after his goal QPR had chances to equalise.
Idrissa Sylla, who struggled up front, was unable to apply the finish after being found by LuaLua's low left-wing cross.
McLaughlin then reacted quickly to race from his line and thwart Washington after he had been put through by Luongo's throughball.
And another LuaLua cross, this time from the right flank, was headed over by Darnell Furlong.
At the other end, keeper Alex Smithies kept QPR in the game by denying Dyer at point-blank range.
Holloway sent on Mackie and centre-back Joel Lynch went up front for the final few minutes in a desperate attempt to salvage a point.
But QPR were unable to do so, with Sylla's weak header wide in injury-time summing up their performance.