Sporting stunned the Bernabeu when David Barral scored against the run of play in the 53rd minute but it only took Manuel Pellegrini's side two minutes to equalise.
Rafael van der Vaart and Xabi Alonso struck in quick succession before Gonzalo Higuain calmed the nerves with a superb solo effort in the 68th as Real claimed their 14th win in 14 home games this season.
They have 68 points from 27 games ahead of champions Barcelona who visit Real Zaragoza on Sunday.
"We only have the league left to fight for and we have the responsibility to win every day," Real midfielder Esteban Granero told reporters.
"We lacked fluidity in the first half but when they scored it stung us and we knew how to react."
A well-organised Sporting made life difficult and there were murmurs of unrest when Barral beat goalkeeper Iker Casillas at his near post. But Real equalised almost immediately in controversial circumstances.
Dutch international Van der Vaart appeared to control the ball with his hand before scoring, after Juan Pablo could only parry Cristiano Ronaldo's free-kick.
Ronaldo then made a prodigious leap and his header from a corner was nodded in at the back post by Alonso.
Argentina striker Higuain put the game beyond doubt, surging towards the area to score his 20th league goal of the campaign.
Sevilla's surprise Champions League exit to CSKA Moscow in midweek appeared to have taken a heavy physical and mental toll as they were well beaten at lowly Espanyol, Argentine striker Pablo Osvaldo scoring a goal in each half.
Manolo Jimenez's side lost wingers Jesus Navas and Diego Capel to injury during the game and remain on 44 points, three points behind third-placed Valencia who are in the final automatic Champions League qualifying spot.
RED CARDS
Athletic Bilbao climbed to sixth with 42 points, above Deportivo La Coruna on goal difference, despite being held 2-2 by visiting Getafe in a stormy encounter at San Mames.
The Basque side took the lead through Pablo Orbaiz after 12 minutes before Getafe levelled through Manu Del Moral in the 32nd.
Bilbao had Orbaiz sent off soon after but went back in front with a Fernando Llorente penalty in the 78th just after Getafe were reduced to 10 men following a red card for Miguel Torres.
Pedro Leon grabbed a late equaliser for the visitors.
Struggling Real Valladolid and Xerez both won to boost their hopes of avoiding relegation.
Valladolid won 2-0 at Deportivo thanks to goals from Nauzet Aleman and Haris Medunjanin.
It was Valladolid's first win in 12 matches and the first under coach Onesimo Sanchez, who replaced Jose Luis Mendilibar at the beginning of last month.
Early strikes from Mario Bermejo and Aythami gave Xerez
