It was a first Tour de France stage win for British outfit Barloworld
The Barloworld rider went over the top of the out-of-category Col du Galibier on his own and held on to his advantage on the flying 32km descent to Briancon.
But the chasers, including race leader Michael Rasmussen, crossed the line just 38 seconds back.
The Dane finished with most of his major rivals, but Alexandre Vinokourov lost more time on the yellow jersey.
The Astana rider, the pre-race favourite, struggled home in a group three minutes and 24 seconds behind Soler Hernandez.
And while the 24-year-old Soler Hernandez described his victory on the 159.5km route across some of race's fabled summits as a "dream", Vinokourov crossed the line in tears.
"I did what I could," said Vinokourov. "The team worked well again and tried to reduce the gap. It was another horrible day for me."
The Kazakhstani's dreams of winning the Tour lie in tatters as he leaves the Alps more than eight minutes off top spot.
Rasmussen increased his advantage over the field to two minutes 35 seconds as young German Linus Gerdemann, who started the day second, trailed in.
Spaniard Alejandro Valverde, who led the pursuing pack across the line from Cadel Evans, Alberto Contador, Iban Mayo and Rasmussen, takes over in second spot with compatriot Mayo staying third.
"Now it's all about the yellow," said Rasmussen, who also tops the King of the Mountains standings.
"I'm still in the lead by almost three minutes and the next big test will be the time trial on Saturday.
"The team did a tremendous job until half way up the Col du Galibier when Valverde attacked a million times, and so did Evans. I chose to follow Valverde."
The stage featured three giant climbs, the first coming immediately as the riders rolled out of Val d'Isere after Monday's rest day.
Spaniard Jose Luis Arrieta attacked early on the 16km ascent and was soon joined by Popovych, who was first across the year's highest climb, the 2,770m Col de l'Iseran.
And the Ukrainian was still at the head of the race as they tackled the Col du Telegraphe after 99km.
By then he had been joined by Jose Ivan Gutierrez, Vladimir Gusev, Mikel Astarloza, Benoit Vaugrenard and Stef Clement and after a brief respite the sextet set out on the gruelling Galibier.
But that was when climber Soler Hernandez, who had been sick at the weekend, struck.
He overtook them in the foothills and never looked back: "I did not know the climbs so I attacked like a fool."
Behind him the big guns cranked up the pressure, with Valverde and Evans repeatedly looking to get away from Rasmussen before the Australian succeeded.
Popovych and Discovery team-mate Contador, who had earlier jumped off the front of the Rasmussen group, crossed the summit a little over two minutes behind Soler Hernandez, with Evans a further 30 seconds back.
But while the leader stayed away despite cycling into a headwind on the road to Briancon, that trio were soon sucked in by the pursuing pack.
And after a frenetic finish for bonus points as the road into continental Europe's second highest city kicked up, the leaders should enjoy an easier day in the saddle on Wednesday on the road to Marseille.
Stage nine result:
Val-d'Isere to Briancon, 159.5km
1. Juan Mauricio Soler Hernandez (Col) Barloworld 4 hrs 14 mins 24 secs
2. Alejandro Valverde (Spa) Caisse d'Epargne @ 38 secs
3. Cadel Evans (Aus) Predictor-Lotto @ 38 secs
4. Alberto Contador (Spa) Discovery Channel @ 40 secs
5. Iban Mayo (Spa) Saunier Duval @ 42 secs
6. Michael Rasmussen (Den) Rabobank @ 42 secs
7. Levi Leipheimer (USA) Discovery Channel @ 42 secs
8. Kim Kirchen (Lux) T-Mobile @ 46 secs
9. Andreas Kloeden (Ger) Astana @ 47 secs
10. Carlos Sastre (Spa) Team CSC @ 47 secs
Selected others:
20. Alexandre Vinokourov (Kaz) Astana @ 3 mins 24 secs
41. Charlie Wegelius (GB) Liquigas @ 6 mins 44 secs
144. David Millar (GB) Saunier Duval @ 28 mins 51 secs
163. Geraint Thomas (GB) Barloworld @ 28 mins 51 secs
164. Bradley Wiggins (GB) Cofidis @ 28 mins 51 secs
Overall standings:
1. Michael Rasmussen (Den) Rabobank 43 hrs 52 mins 48 secs
2. Alejandro Valverde (Spa) Caisse d'Epargne @ 2 mins 35 secs
3. Iban Mayo (Spa) Saunier Duval @ 2 mins 39 secs
4. Cadel Evans (Aus) Predictor-Lotto @ 2 mins 41 secs
5. Alberto Contador (Spa) Discovery Channel @ 3 mins 8 secs
6. Christophe Moreau (Fra) AG2R @ 3 mins 18 secs
7. Carlos Sastre (Spa) Team CSC @ 3 mins 40 secs
8. Andreas Kloeden (Ger) Astana @ 3 mins 51 secs
9. Levi Leipheimer (USA) Discovery Channel @ 3 mins 53 secs
10. Kim Kirchen (Lux) T-Mobile @ 5 mins 6 secs
Selected others:
21. Alexandre Vinokourov (Kaz) Astana @ 8 mins 5 secs
75. Charlie Wegelius (GB) Liquigas @ 56 mins 45 secs
99. David Millar (GB) Saunier Duval @ 1 hr 10 mins 7 secs
152. Bradley Wiggins (GB) Cofidis @ 1 hr 34 mins 23 secs
160. Geraint Thomas (GB) Barloworld @ 1 hr 37 mins 31 secs
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Profile of stage 9, Val-d’Isère to Briançon. 
Mauricio Soler of Colombia has won stage 9 of the 2007 Tour de France. Michael Rasmussen of Denmark retains the overall lead.

The 159.5 km stage 9 began with a cold start to the Hors Categorie climb up to the Col de l'Iseran (15 km at 6%), followed by the Col du Télégraphe and the Col du Galibier (12 km at 6.7% and 17.5 km at 7%) with a 32 km downhill finish in Briançon.

The Colombian Barloworld rider was the first to top the peak of Col du Galibier and held on during the downhill finish. The chase group finished 38 seconds behind him.

Soler was excited by his stage victory: "It’s an incredible day. I’m living out a dream. I worked very hard to arrive at the finish on my own and I received the superb prize for that effort. I wanted to achieve something for myself in my Tour debut and at 24 years of age, I’ve been able to stamp my name on a stage. Nobody believed I could win here, not even me."

Pre-Tour-favorite, Alexandre Vinokourov, who has been struggling since he crashed on stage 5, lost nearly three minutes the in chase for the yellow jersey and is now in 21st place overall.

"I did what I could," said Vinokourov. "The team worked well again and tried to reduce the gap. It was another horrible day for me."

Linus Gerdemann, who surprised everyone in stage 7, fell out of the top ten overall and had to surrender the white jersey to Alberto Contador.