The 22-year-old was split five, three strokes below par, before the final round of the European Tour competition Skaftö Open.
Then she hit with seven birdies, landed on ten under par and climbed up to a split second place - one stroke behind winning Pauline Roussin Bouchard from France.
Beatrice Wallin became the second best Swede in fifth place, seven under par while Ingrid Lindblad, who was second before the final round, lost to sixth place after a heavy 69 round.
The first professional competition
The competition was Linn Grant's first in his professional career - and it was a special moment for the Swedish future promise.
- It was great fun to play today.
I have felt the last two days that there were some better games to come and I got it out today, she says.
It was not entirely obvious that Grant would become a professional right now.
She had two years left in college in Arizona and players usually wait until the turn of the year.
But because of the pandemic, she felt the timing was right.
- The idea was to go back to school a few weeks ago, qualify for the autumn and become a professional in January.
But there were some changed plans.
There were some new decisions from the school regarding the pandemic and then I thought it was better to become a professional now, she says.
As Grant has not yet qualified for any of the major tours, the autumn schedule is quite sparse so far.
- I will play in Kristianstad (Creekhouse Ladies Open) next week, but then I do not know much more than that I will qualify in October, I hope to get some invitations and play on, she says.