Whiley followed up her opening win over top seed Yui Kamiji with a 6-3 7-5 success over German Sabine Ellerbrock.
“It was so important to follow up yesterday’s win – I don’t want to be a one-hit wonder,” she told BBC Sport.
Her compatriots Andy Lapthorne and Gordon Reid kept alive their hopes of reaching the last four in their events.
US Open quad singles champion Lapthorne, the world number two, defeated Lucas Sithole of South Africa 7-5 6-1 and will face world number one David Wagner in his final pool match on Friday with the winner going through to the final to face Australia’s Dylan Alcott.
“I’ve won some big games against David this year so there is no reason why I can’t go out tomorrow and do it again,” said Lapthorne. “We both know what we need to do and we are both under pressure.”
Men’s world number three Reid was a comprehensive 6-2 6-2 victor over Frenchman Stephane Houdet, ranked one place above him.
Reid, who lost to Joachim Gerard in his first round-robin game, will face another French player Nicolas Peifer on Friday with all four players still in with a chance of reaching the semi-finals.
“In my opening game I wasn’t aggressive enough and I rectified that today,” said the Scot.
“I’ve struggled against Stephane in the past but I played how I wanted to play today and came away with the result.”
Whiley, who was seeking a first win over Ellerbrock in 2014, recovered from an early break to go 5-3 up before showing some good skill to hold again and take the opening set.
Whiley dug deep and edged 6-5 ahead, and on her third opportunity to serve for the match finally managed to convert her first match point when a drop shot trickled over the net.
“I was really lucky on match point because the drop shot was accidental. I mishit it and it just managed to go in,” admitted Whiley, who will face Sharon Walraven in her final pool game on Friday before Saturday’s semi-finals.
“I started to feel really tired towards the end and I was losing energy so I’m really pleased I was able to push myself and get that little bit extra to get over the line.
“I knew I needed to finish the match off in two sets because I felt I wasn’t going to last for three.”