The 32-year-old Welshman, who is chasing his first Grand Tour victory, leads team-mate Froome by two minutes and 31 seconds with four stages left.
Thomas’ closest General Classification rival is now Dutchman Tom Dumoulin, who is one minute and 59 seconds behind.
Nairo Quintana held off UAE Team Emirates’ Dan Martin to win the 65km (40-mile) stage.
Featuring a Moto GP-style grid start, the shortest stage of the modern era began with Thomas on his own in front of the rest of the field.
After three brutal climbs in quick succession, separated by twisting technical descents, he had strengthened his hold on the yellow jersey with a commanding ride that showed his all-round ability and no sign of weakness.
Only four stages separate him from the podium in Paris.
With Thursday’s day on the flat expected to be a sprint contest, Friday’s racing, which includes an ascent of the Col du Tourmalet, looks like being the last significant risk to Thomas’ bid for the yellow jersey.
It is followed by an individual time trial and the ceremonial final stage on the Champs Elysees on Sunday.
World cycling chief David Lappartient has responded to Team Sky boss Dave Brailsford’s claims that the abuse of his team and riders is a “French cultural thing”.
Speaking prior to the start of the Tour de France’s 16th stage, the French president of the International cycling Union (UCI), told AFP: “He’s not doing his riders any favours.
In what has been an evenful and controversy-ridden cycling race, Froome has been spat at and manhandled, while Thomas has been booed off the podium and some of Sky’s staff have also had to face abuse during the opening 15 stages.
Froome, in particular has had to deal with far more abuse than his Welsh teammate. While aiming for his fifth Tour de France title, he was the subject of an investigation because a sample from his 2017 Tour of Spain victory revealed twice the permitted amount of salbutamol.
Froome, however, was allowed to race after the UCI dropped their case against him.
Brailsford lashed out at the treatment of his team, in France in particular, on Monday while clarifying that there was no ill-treatment by fans at the Giro d’Italia, which Froome won last May.
“Chris’s case was open when we raced in Italy. And they were fantastic, the Italians (fans),” said Brailsford.
“It seems to be the thing that’s done here. It just seems to be a French thing. A French cultural thing really.”
Lappartient added: “I can understand he (Brailsford) is annoyed the public are not passionate about his team and that they’ve been whistled.
“But that’s no reason to hit out at the French public. Hasn’t Mister Brailsford noticed it’s not just French people on the side of the road?
“He should not be making this about nationality. It’s pointless, and he mustn’t forget everything that France and the Tour de France have given him.”
It was a dramatic end to a stage which had been stopped at one point as riders were affected by a spray used by police to break up a farmers’ protest on the road from Carcassonne.
Mitchelton-Scott’s Yates led on the descent into Bagneres-de-Luchon after attacking three kilometres before the summit of the Col du Portillon, cresting the mountain with a 22-second advantage.
But the 25-year-old Lancastrian crashed with 6.5km to go, allowing Quick-Step Floors’ Alaphilippe to zip by and take his second stage win of this Tour.
Yates was quickly back on his bike, and followed home Bahrain-Merida’s Gorka Izagirre to finish third.
The main contenders crossed the line in a group some nine minutes after Alaphilippe to mean there is no change at the top of the General Classification.
Team Sky’s Geraint Thomas continues to lead by one minute and 39 seconds from team-mate Chris Froome, with Team Sunweb’s Tom Dumoulin a further 11 seconds behind.
Several riders, including Thomas and Froome, needed treatment after being affected by what was thought to be tear gas used by police to break up a farmers’ protest early in the stage.
The protestors had rolled large hay bales into the road 29 kilometres into the 218km stage, and then clashed with police who tried to remove them.
After a spray was used by officers, it appeared to get into the eyes of several riders, with world champion Peter Sagan also among those affected.
The race was stopped completely while they received medical attention and washed their eyes. After a 15-minute interval the race resumed with a short neutralised section before the flag was dropped once again 33km into the stage.
Farmers’ protests are nothing new at the Tour, but the incident will add to the intense security situation in this year’s edition.
Froome was jostled and spat at on Alpe d’Huez, while 2014 winner Vincenzo Nibali saw his race ended after he was brought down in a tangle with a fan on the same mountain.
Former world champion Philippe Gilbert, meanwhile, got back on his bike to continue Stage 16 despite a spectacular crash that sent him flying over a wall.
Gilbert, a Quick-Step colleague of Alaphilippe, was 57.2km from the finish and in the lead of the race when disaster struck.
Negotiating a left-hand bend at speed, the Belgian failed to brake in time, skidded and was sent flying head first over a parapet and into a ditch.
The former Tour of Flanders and Liege-Bastogne-Liege winner was helped back up on to the road and given first aid before resuming the stage in the company of a group of frontrunners.
Although shaken, the 36-year-old looked to have suffered only bruises and scratches.
Medical services which are on hand throughout the race attended to Gilbert’s injuries as he rode alongside the doctor’s car.