Rebecca Peterson won according to plan against the Norwegian Malene Helgø in the first round in Båstad and was up against Leolia Jeanjean in the second round.
Peterson and Jeanjean, ranked 143, both won their serve games in the beginning.
At the position 4-4, the Frenchwoman broke Sverigeettan's serve and finally stood as the set winner 6-4.
The second set was a thriller where Peterson was down 1-4, just two games away from a loss.
Then something lit up in the Swede that turned the match around with five straight games, finally 7-5.
She then continued on the beaten path and finally stood as the winner with 2-1 in sets (4-6, 7-5, 6-3) in a match that lasted two hours and 28 minutes.
In the quarterfinals, Peterson will face American Lauren Davis.
Mirjam Björklund, who has had something of a breakthrough this year when she qualified for both the French championships and Wimbledon, has been knocked out.
The 23-year-old, ranked 125th in the world, lost in two straight sets, 2-6, 3-6, against the Spaniard Rebeka Masarova, ranked 146th.
Caijsa Hennemann gave 100-ranked Hungarian Panna Udvardy something to bite into the introduction.
In the first set, the Swede was equally 3-3 in the game but was defeated 6-4.
Udvardy, on the other hand, showed a class difference in the second set and won the match in two straight sets, 6-4, 6-2.
Hennemann barked on from the first round against much higher ranked Mexican Renata Zarazua.