World number five Whiley, from Ickenham, survived losing the first set to win 6-7 6-4 6-3 against the number two seed.
Whiley has won six major doubles titles in her career but had never made it to a singles final, although this year it was all she had left to play for after defeat in the doubles on Friday.
Having lost the first-set tie-break 7-1, she bounced back to take the next set and then won the decider in a match which lasted just over two hours and 20 minutes.
She will now meet the defending champion, and her close friend and doubles partner, Yui Kamiji in Sunday’s showpiece.
Eastcote’s Andy Lapthorne bowed out of the quad singles after a comprehensive defeat to David Wagner, 6-1 6-0, the match over in 37 minutes.