The pair lead by one over Taiwan’s Candie Kung with South African Ashleigh Buhai another shot back and on her own in 4th place.
Australia’s Minjee Lee improved her position on day two with a round of 66 to be in a share of 7th place and six shots from the lead, a position she shares with amongst others Brooke Henderson.
Amongst the other Australians Sarah Jane Smith is 39th, Sarah Kemp 46th, Su Oh recovering from an opening round of 75 with 67 today to be 63rd a position she shares with Katherine Kirk.
All five of the Australians in the field therefore made the cut.
For Ko the resurgence in form is particularly welcome given the looming final major of the year next week in France (The Evian Championship) and that she will play the McKayson New Zealand Women’s Open Championship in three weeks’ time, a tournament where her being in contention will play a significant role in its success.
"There’s a lot of great vibes here but I still have a whole 18 holes to go tomorrow," said Ko. "I think the key was that I was enjoying being in this position again and being able to hit some good shots and give myself some good looks for birdies.
“When you are doing that it builds your confidence and you are not dwelling on whether you are going to hit a bad shot or a good shot. That’s been the mindset I have gotten into the last few months and it is nice to be able to get out of that.”
Thompson played in the afternoon on day two and added a round of 66 to her stunning opening 63 to join Ko late in the day.
The battle between Ko and Thompson tomorrow promises to be a fascinating one between a former World Number One who appears to have gotten things back on track and the very much in form Thompson who is perhaps on track to get to number one before too long.