The Durban side appeared destined for a draw when Lyon scrumhalf Baptiste Couilloud converted a late try to level the scores at 33-33. However, the Sharks refused to settle for a share of the spoils, with Bester crossing after the final hooter to snatch a memorable win at the Stade de Gerland.
The result marked a significant start to the Sharks' European tour, particularly after they failed to win a match on the continent last season. Lyon had also eliminated them from the competition in the last 16 two seasons ago.
Pietersen was pleased with the collective effort and determination his players displayed throughout the contest.
"If you look at the game, we deserve this win," he said. "We've got some really special players in our group and it was a squad effort.
"There was fight for 80 minutes in the game and to finish it off like that was truly special."
The victory, however, carried a deeper meaning for the Sharks following the sudden death of former player Hyron Andrews in France on Friday.
Andrews spent a decade with the Durban union between 2014 and 2024, making more than 100 appearances before spells with Sale Sharks and the Lions. The 31-year-old had recently joined the Johannesburg-based franchise and featured in their opening three United Rugby Championship matches this season.
Pietersen acknowledged the emotional circumstances surrounding the match and dedicated the victory to the former Sharks lock.
"Today is a really special one. Not just the rugby, but also with Hyron passing away yesterday. It's quite emotional. We'll definitely dedicate this win to Hyron," he said.
For the Sharks coach, the performance also offered an encouraging indication of the togetherness he wants to establish within the squad during their time abroad.
The team will continue their tour with URC fixtures against Cardiff and Munster over the next fortnight, with rested Springboks expected to join the group.
"We want to build connection on tour, we want to show character, and we want to take our identity overseas," Pietersen said.
"As the head coach, that's all you can ask for, guys to fight for the badge, fight for identity, and fight for each teammate."