Rockbottom QPR beat Chelsea 1-0 on Wednesday night, while Liverpool demolished Sunderland 3-0 at Anfield and Everton won 2-1 at Newcastle.
Harry Redknapp's Rangers picked up only their second Premier League victory of the season as they stunned European champions Chelsea at Stamford Bridge.
Former Blues winger Shaun Wright-Phillips scored the only goal with 12 minutes left and although Rangers remain bottom on goal difference, they are now five points from safety.
Luis Suarez struck twice as Liverpool beat Sunderland 3-0 at Anfield.
Raheem Sterling put the hosts ahead after 19 minutes before the Uruguayan striker's brace secured the points to take the Reds up to eighth.
Substitute Victor Anichebe's scored the winner for Everton as Newcastle's poor form continued with a 2-1 defeat at St James' Park.
Papiss Cisse gave the hosts the lead in the second minute before Leighton Baines' thunderbolt free-kick levelled the scores two minutes before the break.
Anichebe, who replaced Steven Naismith in the 58th minute, finished from close range on the hour to send the Toffees fifth.