Who says the British can't play on clay?
Norrie, 29, slipped perilously close to dropping out of the top 100 before reaching the Geneva final and then the Roland Garros last 16 for the first time.
Draper reached the fourth round and Jacob Fearnley advanced to the third round on his debut - losing to Norrie - while Katie Boulter and Sonay Kartal both earned their first main-draw wins.
Boulter, Emma Raducanu and Kartal each continued their upward trajectory in the world rankings, with Kartal now a top-50 player for the first time.
Doubles pair Neal Skupski and Joe Salisbury continued their progress a pairing by reaching the men's final, while Alfie Hewett was runner-up in the wheelchair singles.
Hewett fought back from heartbreak, though, to clinch a sixth successive doubles title with partner Gordon Reid.
And 16-year-old Hannah Klugman underlined her huge potential by becoming the first Briton to reach the junior final in almost 50 years.