Levante missed the opportunity to clamber into the Primera Liga's top four on Thursday, while Espanyol prevailed in a basement battle.
Elsewhere, Real Sociedad stretched their unbeaten run after seeing off 10 men on home soil.
Levante entered their latest fixture sat just a point adrift of the UEFA Champions League, but ended it stuck in sixth spot following a 3-0 defeat at Rayo Vallecano.
Iganacio Martinez Nacho broke the deadlock for Rayo on 59 minutes, before the points were wrapped up late on.
With Levante chasing the game, Piti doubled the hosts' lead 10 minutes from the end and Franco Vazquez stepped off the bench to add a third in stoppage time.
Espanyol and Deportivo La Coruna locked horns in a tussle between the division's bottom two, and it was the Catalan outfit that emerged victorious.
Both sides had gone six games without success prior to their midweek encounter and were facing up a relegation dogfight.
Espanyol sprang out of the bottom three, though, courtesy of experienced Portuguese playmaker Simao and substitute Christian Stuani, with the pair netting after 31 and 88 minutes respectively.
Real Sociedad are very much in the hunt for European qualification following a 2-1 victory over out-of-sorts Sevilla.
Sociedad have now gone seven games without defeat, while Sevilla are five without a win.
Former Arsenal striker Carlos Vela broke the deadlock at Anoeta Stadium after 18 minutes, only for Gary Medel to restore parity four minutes into the second half.
Alberto de la Bella edged Sociedad back in front on 69 minutes and any hope Sevilla had of finding a route back into the tie evaporated five minutes later when Coke picked up a second yellow card.
Gold revealed during a question and answer session on Twitter that he expects the pair to remain part of Sam Allardyce's plans throughout the 2012/13 campaign.
Diame has been strongly linked with a January switch elsewhere, having shone for the Hammers since linking up with them as a free agent over the summer.
Carroll, meanwhile, is on a season-long loan from Liverpool, but it has been suggested that agreement could be cut short due to the striker's inability to steer clear of injury.
A switch elsewhere in the New Year has also been touted for the England international, which would bring an end to his stay in the East End.
Gold, though, has rubbished claims that a loan could be cancelled due to injury and when asked if Carroll will end the season with the Hammers, he said: "Yes, I believe so."
The Hammers supremo was later pressed on whether there was any truth in reports that Arsenal have expressed an interest in Diame.
He said: "I'm not aware of any offers."
He then went on to say 'I believe so' when asked if Diame would still be a West Ham player next summer.
