The 29-year-old was bogey free as he moved to nine under alongside countryman Marcus Kinhult after carding the lowest round of the week so far at Education City Golf Club.
Björk had the world at his feet after claiming a maiden European Tour win at the Volvo China Open in 2018 en route to finishing in Europe's top 20 at the end of the campaign.
He had just one top ten in 2019 but has felt recently that his game is returning to him and certainly showed it in Doha.
“I have been struggling a lot lately but I have been starting to feel last week that the game was getting a bit better," he said. "I played quite good yesterday but did not get the putts to drop, so I don’t know.
"I just got in a really good flow from the start, hitting almost every fairway, kind of firing at the pins so it just felt really good.
“I took advantage of the really calm weather and when you feel like the swing is really there and there is no wind, you can aim at the pins and I got a lot of good chances.
“Like I said, I have been coming off quite a tough stretch, so it was a lot of fun to actually feel the flow again and maybe my best round tee to green since I won two years ago. It was fun to get that feeling again because it was a long time ago."
Kinhult had an eventful 65 with an eagle, six birdies and two bogeys and revealed he had been to the Qatar Open table tennis as part of his preparations - and planned to return.
“I played practise rounds as always and I went to the table tennis actually, it is about ten minutes away, so that was my preparation for the week," he said.
The reigning Betfred British Masters champion is staying with his father and coach Martin this week in Qatar and the former professional is still a big influence on his son.
“My dad will always be (a huge mentor in his life) and he is here this week," he said. "It’s his first tournament of the year and we are staying together, so it’s nice to have him out here."