The British number one moved up three places despite losing to German Julia Goerges in the French Open first round.
Durie, who won two WTA singles titles in 1983, achieved a career-high ranking of five a year later.
Konta, 25, faces American Victoria Duval in the first round of the Nottingham Open on Monday at 12:00 BST.
Johanna Konta has reached her highest career ranking of 18, the first British woman to break into the top 20 since Jo Durie in 1983.