Hansen, the overnight leader, bogeyed his last three holes for a 1-under 71 at Gut Larchenhof, falling into a tie with Bjorn at 12-under 204.
They held a one-shot lead on Alastair Forsyth, who posted nine birdies, an eagle and one bogey for a 62 that was still two shots off the course record. He stood at 11-under 205.
Lee Westwood, who opened with a 61 on Thursday, shot a 72 in the third round and was tied for fourth place with Richard Green (66) and Simon Khan (69) at 10-under 206.
Overall, there were 11 players within five shots of the leaders. Tournament host Bernhard Langer was among them after carding a 70 to join Philip Archer (66) and Niclas Fasth (69) at 9-under 207.
Bjorn had three birdies on both the front and back nines, posting a bogey-free round to climb from a tie for sixth place into a share of the lead. He is playing for just the second time in two months.
'I've never had a summer holiday since I was 14 and now with three kids I really wanted to spend some time with them,' said Bjorn, 36. 'I was working very hard but things were going nowhere and it was nice to take some time out when the kids were out of school.'
Sunday, Bjorn will be seeking his 10th European Tour victory and first since the 2006 Irish Open.
'I'm at a crossroads in my career. I've made a conscious decision about how I want to swing the club and play the game, but I have no goals whatsoever,' he said. 'I just want to play some golf and enjoy myself and this is a huge step forward. I haven't had many rounds in the 60s and you're not going to compete in tournaments if you don't shoot low.'
Bjorn benefited from Hansen's late-round collapse after the onetime European Tour winner lost a three-shot lead with three straight bogeys to end the day. Hansen avoided a double-bogey at the 18th by scrambling for a bogey after hitting his tee shot into the water.
He almost knocked his third shot in the water as well.
'I lost a little bit of touch over the last few holes, and it cut me to the bone. I didn't feel really comfortable, and I pulled a few shots, but I managed to hit a great chip on the last,' said Hansen.
'It gave the crowd a bit of excitement.'
Sunday, the same crowds will see two countrymen play together for the first time since they finished near the bottom of the World Cup last December.
'Soren is a huge talent. He has sorted his putting out this summer, which was always the weak part of his game,' said Bjorn. 'I've always pushed him harder and harder to make him realize how big a talent he is. All he needs to do is win another tournament. I hope tomorrow it's me winning, but if it's not me, then I hope it's him.'
Added Hansen, 'Thomas has not been playing to his potential this year, but a Thomas Bjorn in form is a very dangerous man, so I will have to play well to beat him.'