Champions Barca had gone two clear with a Lionel Messi-inspired 3-1 home win over third-placed Villarreal on Saturday and Jose Mourinho's unbeaten Real side struggled to find a goal against a determined Gijon, whose goalkeeper Juan Pablo was on inspired form.
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The match at a hostile Molinon had taken on added significance for the Asturian club after Mourinho suggested they had fielded a weakened side at Barca earlier this season because they did not seriously believe they could win.
The combative Portuguese had to watch the match from the stands after being sent off in Wednesday's King's Cup win over Real Murcia and banned from the bench for two matches.
Real's Argentina forward Higuain came close to finding the net in the 10th minute when his angled shot hit a post.
Pablo produced three superb saves in the second half to deny Angel Di Maria, Higuain and substitute Karim Benzema but it was his handling error that led to Real's goal in the 82nd minute.
He blocked a headed Benzema effort but palmed the ball straight to Higuain who gleefully tapped the ball over the line from close range.
Gijon nearly equalised a minute later but Real keeper and captain Iker Casillas flung himself full length to keep out a powerful downward header from David Barral.
It was Real's sixth straight league win and puts them on 29 points from 11 matches. Barca, who host Real for the first of the season's two "Clasicos" on November 29, have 28 and Villarreal are on 23.
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Tension had mounted between Real and Gijon in the build-up to the match following Mourinho's comments.
Gijon coach Manuel Preciado, whose side lost 1-0 to Barca at the Nou Camp in September, was furious at what he described as a lack of respect and slammed the Portuguese at a news conference.
Real released a statement saying they regretted Preciado's comments and cancelled a news conference that Mourinho's assistant, Aitor Karanka, was due to have given on Saturday.
"It was a tough game, especially considering all that had been said this week," Casillas said in a television interview.
"I respect others' opinions but I don't share them and I defend my coach, who is the best," he added.
Preciado earned backing for his stand from La Liga coaches, including Espanyol's Mauricio Pochettino and Villarreal's Juan Carlos Garrido, and said he was "super proud" of what he said about Mourinho.
"Maybe not of the way I said it because I am very crude but the basic message yes," he told a news conference. "I would do the same thing again."
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