Harry Redknapp's side were billed as pre-season favourites for the title, but automatic promotion now looks unlikely after the London club suffered a fifth defeat in their last eight league games on Tuesday.
Republic of Ireland defender Dunne was given his marching orders 12 minutes before half-time for a professional foul on Leon Best and there was no way back for QPR after Chris Maguire converted the resulting penalty.
Best added a second goal six minutes into the second half and Lewis Buxton made sure 19 minutes from time as QPR failed to secure the point needed to leapfrop Derby County into third place.
Fifth-placed Wigan Athletic looked set to make up more ground on the sides above them, but their eight-game winning run in all competitions came to an end when they were held to a dramatic 3-3 home draw by struggling Yeovil Town.
Nick Powell put Uwe Rosler's side in front, but there were five goals in the last eight minutes as Ishmael Miller's quickfire double put Gary Johnson's side in front. James McArthur then equalised and Byron Webster's own-goal after 88 minutes looked to have won it for Wigan.
Yeovil refused to feel sorry for themselves, though, and Luke Ayling had the final say when he prodded home a corner from close range to salvage a precious point that still leaves the Somerset club second-bottom of the table, but will give them belief they can avoid the drop.
There was also a crucial late goal at The Valley, where Jose Riga celebrated his first victory as Charlton Athletic manager courtesy of Dorian Dervite's last-gasp winner against Bournemouth.
The defender scored the only goal of the game to move Charlton out of the relegation zone on goal difference ahead of London rivals Millwall.
League One leaders Wolves' 10-match unbeaten run was ended with a 2-1 defeat at Crawley Town.
James Henry put Kenny Jackett's charges in front after 25 minutes, but Billy Clarke equalised two minutes later and Matt Tubbs' strike brought Wolves back down to earth to ensure they only lead second-placed Brentford by one point and the London outfit have a game in hand.
Shrewsbury Town were beaten 1-0 at Colchester United in the other third tier game played on Tuesday,
Reuben Reid scored twice as Plymouth Argyle manager John Sheridan gained revenge against his former club Chesterfield, who slumped to a 2-1 defeat at Home Park that ensured they slipped off the top of the table.
Rochdale replace the Derbyshire club at the summit after they coasted to a 3-0 victory at relegation-threatened Northampton Town.
Bottom-of-the-table Torquay United enhanced their chances of staying up by beating Bury 2-1, Accrington Stanley hammered Morecambe 5-1 in a Lancashire derby and Cheltenham Town drew 1-1 with Wycombe Wanderers at Whaddon Road.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get FourFourTwo Newsletter
The best features, fun and footballing quizzes, straight to your inbox every week.