While fellow veterans Darren Clarke and Colin Montgomerie found themselves in contention after rounds of 69 and 70 on Thursday, Bjorn and Jimenez found themselves at the wrong end of the leaderboard in the elite 36-man event at Durban Country Club going into the second day of the Volvo Golf Champions on Friday.
Jimenez chipped in for a birdie on the first but also carded two double bogeys and three bogeys in his 76, while Bjorn fared even worse with a 79 as strong winds swept across the course which is just yards from the Indian Ocean.
Bjorn, 42, is currently second in the European Ryder Cup points list after his victory in the Nedbank Challenge at the end of the last year, while the 50-year-old Jimenez is just outside the automatic qualifying places after retaining his Hong Kong Open title in December.
The duo were first out when play resumed this morning - along with an amateur partner who was among 18 people who had won the right to compete in a team event for the day - and quickly improved their situation.
Jimenez again birdied the first and picked up another shot on the fourth, while Bjorn birdied the third, fourth and eighth before both players dropped a shot on the ninth.
A birdie from Jimenez on the 12th got him back to two over for the tournament, while Bjorn picked up a shot on the next to improve to four over.
France's Raphael Jacquelin held the overnight lead after a flawless opening 67, with defending champion Louis Oosthuizen a shot behind.
Jimenez was unable to find any further birdies and signed for a 70 to finish two over, but Bjorn picked up shots on the 14th and 17th and despite a bogey on the 16th he returned a 68 to lie three over.
There were also plenty of birdies at the top of the leaderboard, Clarke picking up shots at the first, third and fourth to briefly claim the lead before Jacquelin regained top spot with birdies of his own on the third and fourth.
At seven under, Jacquelin led by one from Clarke, with France's Victor Dubuisson another shot back after chipping in for an eagle three from short of the green on the par-five third.