Wiggins, who took the lead with a triumph in the second stage individual time trial on Monday, finished fifth in the toughest stage of the race and extended his overall lead to 30 seconds going into the final two stages this weekend.
Orica rider Chavez powered solo to win the 152km stage that ended in the San Gabriel Mountains northeast of Los Angeles in a time of 4 hours 9 minutes 13 seconds.
On a day when temperatures again soared into the upper 30s Celsius, the Colombian climber attacked from a small group in the last five kilometres of the final ascent, putting some room between himself and David de la Cruz of Spain and American Tom Danielson.
De la Cruz finished second, 13 seconds back, and Danielson was third, 41 seconds adrift.
Briton Adam Yates was fourth, 53 seconds back, with Wiggins fifth in the same time.
“Surprisingly, I was pretty comfortable with four kilometres to go,” Wiggins said. “Then the altitude kicked in.”
He had enough left, however, to hold off his nearest rival in the overall classification, Australian Rohan Dennis.
Garmin’s Dennis finished seventh, 55 seconds off the lead to surrender two seconds to Wiggins overall.
“We had Tommy D off the front, so we were watching what Sky was doing,” Dennis said.
“Hopefully, they were riding hard and they would just blow up like they did on Diablo. But it wasn’t quite as steady an uphill, there was some downhill to recover. When we got to the last kilometre I don’t think I’ve pedaled like that for awhile.”
The race continues Saturday with a 143km stage from Santa Clarita to Pasadena that features two significant climbs, with the final stretch all downhill.
The tour concludes on Sunday in Thousand Oaks, in rolling countryside west of Los Angeles.
STAGE SIX RESULTS
1. Jhoan Esteban Chaves Rubio (COL/ OGE) 4:09:13
2. David De La Cruz Melgarejo (ESP/ TNE) +13
3. Thomas Danielson (USA/ GRS) +41
4. Adam Yates (GBR/ OGE) +53
5. Bradley Wiggins (GBR/ SKY) +53
6. Peter Stetina (USA/ BMC) +55
7. Rohan Dennis (AUS/ GRS) +55
8. Jack Bobridge (AUS/ BEL) +1:07
9. George Bennett (NZL/ CAN) +1:15
10. Lawson Craddock (USA/ GIA) +1:16
11. Laurens Ten Dam (NED/ BEL) +1:21
12. Janier Alexis Acevedo Colle (COL/ GRS) +1:24
13. Daan Olivier (NED/ GIA) +1:32
14. Joseph Lloyd Dombrowski (USA/ SKY) +1:32
15. Gregory Obando Brenes (CRC/ JSH) +1:38
16. Carter Jones (USA/ OPM) +1:41
17. Tiago Machado (POR/ TNE) +1:46
18. Haimar Zubeldia Agirre (ESP/ TFR) +1:49
19. Daniel Alexander Jaramillo Diez (COL/ JSH) +1:55
20. Chad Haga (USA/ GIA) +2:09
1. Bradley Wiggins (GBR/ SKY) 22:03:42
2. Rohan Dennis (AUS/ GRS) +30
3. Lawson Craddock (USA/ GIA) +1:48
4. Tiago Machado (POR/ TNE) +2:02
5. Adam Yates (GBR/ OGE) +2:14
6. Peter Stetina (USA/ BMC) +2:30
7. Jhoan Esteban Chaves Rubio (COL/ OGE) +2:39
8. Laurens Ten Dam (NED/ BEL) +3:01
9. Janier Alexis Acevedo Colle (COL/ GRS) +3:05
10. David De La Cruz Melgarejo (ESP/ TNE) +3:06
11. Carter Jones (USA/ OPM) +3:19
12. Haimar Zubeldia Agirre (ESP/ TFR) +3:45
13. Matthew Busche (USA/ TFR) +3:57
14. George Bennett (NZL/ CAN) +4:11
15. Thomas Danielson (USA/ GRS) +4:27
16. Daan Olivier (NED/ GIA) +4:51
17. Gregory Obando Brenes (CRC/ JSH) +7:30
18. Kristijan Koren (SLO/ CAN) +8:00
19. Thomas Damuseau (FRA/ GIA) +8:23
20. Daniel Alexander Jaramillo Diez (COL/ JSH) +9:28