World number five Whiley, from Ickenham, beat defending champion – and doubles partner – Yui Kamiji 6-4, 0-6, 6-1 in a match of fluctuating fortunes.
The pair, close friends, have won six major doubles titles together but found themselves on opposing sides of the net.
Whiley saw an early break disappear in the first set, only to regroup and take the last two games to seize the initiative.
Kamiji raced through the second set, but Whiley returned from a comfort break before the final set with a renewed focus and stormed into a 5-0 lead.
Whiley then had her first five match points saved before Kamiji pulled a game back, but another thrilling final game eventually saw the Brit clinch a famous victory on her ninth championship point.
“It really hasn’t sunk in that I’ve done it,” said Whiley.
“It was so strange playing Yui as she’s my best friend and we’ve achieved so much in doubles together but it means I know her game so well.
“I felt bad seeing her crying at the end but that’s tennis and I knew I could win it. I kept telling everyone that I could do it in singles as well and now I’ve finally proved it.”