She is joined in the semi-finals fellow Briton Watson, who had won her second match of the day only minutes earlier.
Denmark's Wozniacki, 26, will in Saturday's final face Karolina Pliskova of the Czech Republic.
Konta, World No.7, suffered a fall during her match against Germany's Angelique Kerber, World No.1, and after being treated on the court she managed to win the match 6-3, 6-4.
'I'm still quite sore through my thoracic spine, ' Konta said. Next week is Wimbledon but I make decisions for my health.
"I'm not thinking about [Wimbledon] right now, I just want to rest well and to make sure that I get my health back to the best place possible".
"And I do see things differently, not only tennis, but moments in the life when I realised it is much more nicer than I saw it before".
In the women's draw, British number one Johanna Konta will start against Taiwan's Hsieh Su-wei, whom she lost to in the first round at the French Open last month.
Drake Bell and Josh Peck's Feud: Everything We Know So Far
Josh who? Drake Bell is busy showing off his abs in Flaunt magazine . 'Josh was really hurt [by the tweets]. One fan even suggested that they are emotionally scarred by the Drake and Josh drama.
Watson was disappointed to bow out but encouraged that her form is improving ahead of Wimbledon, where she will face Belgium's Maryna Zanevska, the world No 117, in the first round.
The third-seeded Pliskova dispatched two-time Grand Slam champion Svetlana Kuznetsova 6-7 (7), 6-2, 6-4 in her quarterfinal. I'm feeling great about my game and got some great match wins under my belt this week.
Kerber, the world number one, has struggled since reaching the top of the rankings, making just one final in 2017 and suffering a number of early exits.
Serena Williams misses the tournament due to her pregnancy, but her sister Venus, a five-time Wimbledon champion has been drawn to play Belgium's Elise Mertens.
"It could have gone both ways, honestly", said Wozniacki, the 2009 champion at Eastbourne.
"It's going to be a tough match".
"She is a good player, has a great volley, mixes it up and serves well on grass, so a lot of credit to her". "So I am really grateful that I am still here and to live the moment".
"She's coming in with a tremendous amount of confidence and hunger to play".