Los Blancos twice trailed to the struggling hosts, but a double from Isco, including a stunner in the 90th minute, ensured that the Madrid giants would move further clear of Barcelona at the summit.
Spanish forward Burgui - on loan from Real Madrid - missed out for the home side through suspension, while Juan Rodriguez and Lacina Traore were both ruled out of action through ankle and foot injuries respectively.
As for Real Madrid, head coach Zinedine Zidane made nine changes to the team that started the first leg of their Champions League quarter-final away to Bayern Munich during the week.
Only Sergio Ramos and Nacho kept their spots, while there was a first La Liga start of the season at left-back for Fabio Coentrao. Marco Asensio, Lucas Vazquez and Alvaro Morata were also among those to come into the XI.
The first opportunity of the match came for Sporting in the eighth minute when Moi Gomez picked out the head of Duje Cop from a wide position, but the striker's downward effort was hacked clear by Nacho at the vital moment, before Vazquez headed a super Danilo cross over the crossbar down the other end.
It was Sporting that made the breakthrough in the 14th minute when Cop allowed a wonderful pass from Mikel Vesga to drop straight onto his left foot, and the striker's volley found a route past Kiko Casilla in the Real Madrid goal.
Real Madrid were behind for less than three minutes, however, with Isco producing a wonderful piece of skill inside the Sporting box before picking out the top corner with a curling effort to level the scores in Gijon.
Morata had a decent chance to send Real Madrid ahead just before the 30-minute mark when he rose above Jean-Sylvain Babin to meet a cross from Vazquez, but the Spain international headed over Ivan Cuellar's crossbar.
Opportunities were few and far between in the latter stages of the first period, however, with a long-range effort from Vazquez, which missed the crossbar, just about the closest either side came to taking the lead.
Real Madrid had a glorious chance to take the lead in the 48th minute when Nacho met a deep free kick from James, but Sporting goalkeeper Cuellar was on hand to make a wonderful point-blank save.
Less than two minutes after Nacho had passed up that big opportunity to send the visitors ahead, Sporting took the lead when Vesga flicked a clever header into the far corner after Casilla had been caught too far off his line.
Los Blancos responded once again, however, with Morata levelling the scores just before the hour mark after rising above the Gijon defence to head a super Danilo cross into the bottom corner of the net.
Danilo came close to scoring Real Madrid's third himself in the 62nd minute after meeting a deep free kick from James, but the Brazilian's header was wide, before Cop just missed the target with a curling effort down the other end.
Mariano Diaz was introduced 20 minutes from time as Zidane looked to complete the turnaround, and a low Marcelo strike was deflected just wide of the post in the 72nd minute as Sporting came under a siege of pressure.
Mariano then came close with a header in the 82nd minute, but Isco proved to be the hero for Real Madrid in the final minute when his brilliant strike from distance beat Cuellar to ensure that Zidane's side would collect another vital three points.
Next up for Real Madrid is the second leg of their Champions League quarter-final at home to Bayern Munich on Tuesday night, while Sporting have a massive league game away to basement side Osasuna next weekend.