The British number one overcame Donna Vekic on Centre Court with a 7-6(4) 4-6 10-8 victory.
There were signs early on that this would be a tight match as both were strong on serve before getting broken in the first set.
Konta had four break-point opportunities to wrap up the opening set, but Vekic worked hard to stay in the game and eventually forced a tie-break.
The Brit managed to edge it after one hour and nine minutes of play, but she wobbled at the start of the second set when her opponent went a beak up at the first time of asking.
Despite Konta pulling a game back, Vekic was much more composed and managed to convert another break point before levelling up on the main stage.
Both players upped their game in the third and final set but as a result cancelled each other out, which made for an agonising battle.
With the set 9-8 in Konta's favour, the 26-year-old soaked up the pressure to convert a second match point and seal a place in the next round of the Grand Slam.