Atletico extend their advantage at the top of the table from one to three points over Real while Barcelona, who now have a game in hand after winning the Copa del Rey final on Saturday, are five points back.
LaLiga: Leaders Atletico Madrid held to stalemate by Getafe, Real Madrid close gap with last gasp Karim Benzema winner
Real Madrid had earlier come from behind to beat Elche 2-1, thanks to a late double from Karim Benzema, with Atletico's stalemate meaning the gap is down to six points between the city rivals.
European football matchday: Chelsea travel to Leeds United; Bayern Munich at Bremen in most-contested fixture
Chelsea are in the fourth Champions League spot, two points ahead of West Ham, who have a game in hand.
After earning a second trip to the spot, Iglesias took it on himself to fire the penalty past Soria for the 84th-minute winner in Seville.
Karim Benzema and Ferland Mendy scored the goals at Valdebebas, with Mendy's finish teed up by his fellow left-back Marcelo, who revelled in his new role.
Real Madrid sit 10 points adrift of Atletico Madrid, who have two games in hand and will stretch the gap to 13 points if they beat beat Celta Vigo at home later on Monday.
The home victory against Getafe left Athletic in ninth place in the Spanish league, closer to the qualification spots for European competitions.
European football matchday: Tottenham play Wycombe for second time in history; Athletic Bilbao host Getafe
A look at what’s happening in European football on Monday
Elche took the lead through Raul Guti in the fourth minute, but Getafe rallied with goals by Marc Cucurella in the 39th minute, Jaime Mata in the 69th, and Angel Luis Rodriguez in the 86th.
European football matchday: West Ham look to avoid another FA Cup upset; Elche host Getafe in LaLiga
Premier League club West Ham will visit Edgeley Park to take on Stockport in FA CUp.
Ibiza made no mistake in dumping out top-flight opposition Celta Vigo, racing into a 3-0 half-time lead over Celta, helped by two goals from Sergio Castel.
Granada moved to within two points of the Champions League places after beating Valencia 2-1 in a feisty match where three players were sent off in six second-half minutes.
LaLiga: Real Madrid recovery halted by three Valencia penalties and own-goal; Real Sociedad remain top
Madrid took the lead through Karim Benzema but presented Valencia with four gifts at Mestalla, including three spot-kicks and an own-goal scored by Raphael Varane, to fall to another surprise defeat.
Silva opened the scoring with a header on Sunday as Real Sociedad beat Celta Vigo 4-1 to take a one-point lead at the top of the league.
Zinedine Zidane made four substitutions at half-time but could not spark a lethargic Madrid into life as his team fell 1-0 at home to newly-promoted Cadiz.
Getafe had only scored once in their opening two games but struck three times in the first half against Betis, who started the day as league leaders.
Karim Benzema, the heart of Madrid’s title run last season, set up Federico Valverde for the 14th-minute opener, and pressured Emerson into scoring an own goal
A look at what’s happening around European football on Wednesday with the resumption of the Europa League's round of 16
LaLiga: Real Madrid move closer to title after win against Granada; Sevilla secure top four spot after Villarreal loss
Madrid can clinch their first title since 2017 on Thursday with a win at Villarreal, or if Barcelona lose points when they hosts Osasuna.
It was the sixth straight loss for Espanyol, and its 11th consecutive league defeat away to Barcelona at the Camp Nou Stadium. It has 24 points from 35 matches — 11 points from safety.