"That was one of the hardest days I've ever had on a bike," Froome said. "I'm really happy with how I came through today. ... It's not easy to follow Quintana in the climbs. He's a light little Colombian who can fly up hills so to cover his attacks definitely wasn't easy."
"But yeah, I was quite ready for more attacks, and I'm quite glad there weren't," he said, adding that it was "quite understandable" that his teammates weren't with him after Saturday's effort.
The Briton kept an eye on his top rivals to win the title in Paris on July 21, including Spaniard pair Alberto Contador, of the Saxo Bank team, and Alejandro Valverde one of five Movistar riders in the front bunch of about two dozen riders.
The Briton was content to let Martin and Fuglsang go ahead, and fight for the stage win. After a brief cat-and-mouse game, Martin wheeled around the Dane before the final bend with about 150 meters to go and held on for his first Tour stage win. Martin is the nephew of 1987 Tour champion Stephen Roche and a cousin of fellow cyclist Nicolas Roche.
"I was confident in the final stretch because I know I have some speed," Martin said, adding he was lucky to have Astana's Fuglsang with him to share the work of holding off the favorites. "I knew I had to be ahead in the last two corners and, when I saw that I was, I knew I could win."
"Luckily I had the legs to finish the job."
They crossed 20 seconds ahead of Froome, two-time Tour winner Contador, and 2011 champion Cadel Evans of Australia, among others. Overall, the top standings didn't change much, except that Sky rider Richie Porte of Australia tumbled from second place overall to 33rd after finishing nearly 18 minutes behind Martin.
Froome's closest challenger is Valverde, who is 1:25 behind. Contador is sixth overall and trails by 1:51. Martin is eighth, 2:28 back.
Froome captured the yellow jersey Saturday by launching a devastating attack in the final climb to win Stage 8, thanks in large part to a strong escort from Sky including Porte, who was second in that stage.
But the fact there were none of his teammates around to help Froome will encourage the other teams that the seemingly unbeatable Sky team may have weaknesses. Tired from their efforts Saturday, the other Sky riders fell back early on and Froome was left to fend for himself.
As is required of the yellow jersey holder after each stage, Froome went straight to anti-doping control after the race. This is the first Tour since Lance Armstrong's fall from grace after he was stripped of his seven Tour titles from 1999-2005 for serial doping.
Froome vouched after his win Saturday that he was "100 percent" clean and was asked on French television after Sunday's stage if he has ever taken a performance-enhancing product.
"No," Froome said. "I trained for many months to arrive here in this form."
With temperatures once again well into the 30s Celsius (above 90 Fahrenheit), Froome found himself isolated on the day's first category 1 ascent up to Col de Mente, where Evans fell 40 seconds behind the yellow jersey group. Then, a breakaway group featuring Ryder Hesjedal, Tom Danielson and Pierre Rolland forged ahead.
Froome's chasing group included Contador, flanked by his Saxo-Tinkoff teammates, while Quintana sat behind Froome.
Once they got over Col de Mente, Valverde attacked on the descent and chased after the breakaway group, prompting Froome to go after him.
The second tough climb was the day's longest about 8 miles up the famed Col de Peyresourde and a new breakaway took the initiative.
Hesjedal, last year's Giro d'Italia winner, and climbing specialist Rolland were still there, joined by Romain Bardet of France and Belgian trio Bart De Clercq, Thomas De Gendt and Jan Bakelants. They were about 40 seconds ahead of Froome's group at the top of Peyresourde.
Quintana's Movistar teammates drove hard at the front of the 20-man yellow jersey group as they chugged toward the third climb in the blazing sun.
Australia's Simon Clarke joined the leaders as the seven-man breakaway started to up the tempo and then broke away on his own up the Col de Val Louron-Azet a 4.5-mile ascent.
Clarke was 1:10 ahead of Froome's group before he sped down a sharp descent to La Hourquette d'Ancizan 6 miles at 7.5 percent gradient.
Froome, meanwhile, tucked in behind four Movistar riders with Quintana riding his wheel for the last few kilometers until the last climb, where the breakaway riders were caught.
French President Francois Hollande was among the spectators, protected from the heat in Tour director Christian Prudhomme's car.
Tuesday is a flat stage for sprinters. Froome will be among the favorites to win Wednesday's time trial on Stage 11.
Tour de France
P Stage 10
Tuesday, 6 a.m.
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