Igiebor pounced to slot home the rebound after Joan Verdu's initial shot had been parried in the 37th minute and there was no way back for Villarreal, who could have moved above Real Madrid and into third in standings with victory at the Benito Villamarin.
The Yellow Submarine's woes were compounded in stoppage time when head coach Marcelino Garcia Toral was sent to the stands after protesting when his side had a penalty appeal turned down.
Adrian Colunga's second-half double inspired Getafe to a shock 2-0 win at Espanyol.
The hosts were looking to bounce back from their first defeat of the league campaign at Villarreal in midweek, but were undone by Colunga's brace.
The 28-year-old fired home in the 73rd minute and again in stoppage time, with both goals coming after excellent work from substitute Pablo Sarabia.
Osasuna's ill-discipline kept them rooted to the foot of the standings as Levante stole a 1-0 victory with a late Jordi Xumetra goal.
Xumetra was quickest to react after Papakouli Diop's 87th-minute penalty was saved by Andres Fernandez and Osasuna's day got worse when substitute Alvaro Cejudo was handed a second caution in injury time.
Elche clinched their first Primera Division victory in almost a quarter of a century after beating Celta Vigo 1-0 courtesy of a second-half Javi Marquez goal.