Wiggins was well positioned at the front of the pack when Frenchman Arnold Jeannesson launched an attack with 700 meters to go. Even though Jeannesson is not a threat for overall victory, Wiggins still chased and isolated himself.
Westra took advantage by surging ahead with a brutal acceleration in the last 300 meters, and Wiggins could not follow him. Westra casually looked over his shoulder as he crossed the line.
Westra moved into second place, six seconds behind Wiggins, but is also not a major threat to the leader.
An early four-man breakaway attacked shortly after the start of the 178.5km mountain stage from Onet-le-Chateau to Mende, which featured three category 1 climbs and ended with a sharp, sinewy ascent up La Croix Neuve.
With nine kms left, the breakaway group was caught up by the chasing pack, with Alejandro Valverde's Movistar team moving the Spaniard into a strong position for a late attack.
Valverde struggled in the first portion of the final climb up, but Wiggins could not shake him off and Valverde beat the Brit in a sprint to the line to take second place in the stage and shave two seconds off Wiggins' lead.
Valverde moved up to fourth place and is now 18 seconds behind Wiggins, who is also targeting victory at the Tour de France in July.
Results on Thursday from the fifth stage of the Paris-Nice race, a 178.5km mountain stage from Onet-le-Chateau to Mende featuring three category 1 climbs:
1. Lieuwe Westra, Netherlands, Vacansoleil-DCM, 4 hours, 52 minutes, 46 seconds.
2. Alejandro Valverde, Spain, Movistar, 6 seconds behind.
3. Bradley Wiggins, Britain, Sky Procycling, same time.
4. Levi Leipheimer, United States, Omega Pharma-Quickstep, same time.
5. Simon Spilak, Slovenia, Katusha, same time.
6. Damiano Cunego, Italy, Lampre-ISD, :16.
7. Arnold Jeannesson, France, FDJ-Bigmat, same time.
8. Sylvester Szmyd, Poland, Liquigas-Cannondale, :24.
9. Rigoberto Uran, Colombia, Sky Procycling, same time.
10. Thomas Voeckler, France, Europcar, :30.
Overall Standings:
1. Bradley Wiggins, Britain, Sky Procycling, 18 hours, 23 minutes, 40 seconds.
2. Lieuwe Westra, Netherlands, Vacansoleil-DCM, 6 seconds behind.
3. Levi Leipheimer, United States, Omega Pharma-Quickstep, :10.
4. Alejandro Valverde, Spain, Movistar, :18.
5. Simon Spilak, Slovenia, Katusha, :37.
6. Tejay Van Garderen, United States, BMC Racing, :39.
7. Maxime Monfort, Belgium, Radioshack-Nissan, :46.
8. Arnold Jeannesson, France, FDJ-Bigmat, 1:06.
9. Sylvain Chavanel, France, Omega Pharma-Quickstep, 1:16.
10. Robert Kiserlovski, Croatia, Astana, 1:21.