Laura Davies, the first-round leader, bogeyed four of her first five holes, but fought back to post a 1-under round of 71. She completed 36 holes at 9-under-par 134, where she was joined by Annika Sorenstam. Wendy Doolan is one stroke further back at minus-8.
Stupples, who picked up her first win at the Welch's/Fry's Championship earlier this year, opened with a birdie at the first. However, she dropped a shot at the very next hole to fall back to minus-4.
The 31-year-old birdied the par-4 fifth at Evian Masters Golf Club for the second straight day. After a par at the sixth, Stupples turned it on.
She dropped in a 5-foot birdie putt at the seventh and came right back to birdie No. 8 from 20 feet. Stupples moved to minus-8 with a two-putt birdie at the par-5 ninth.
Stupples closed a run of four straight birdies with an 8-foot birdie putt at the 10th to get to minus-9. She posted six consecutive pars before a birdie at the 17th gave her a share of the 36-hole scoring record and the overnight lead. Maria Hjorth set the 36-hole record of 134 in 2001 and Sorenstam matched the mark in 2002.
'I enjoyed my group and I had a later time today, so the greens rolled fabulously,' said Stupples. 'I really felt I didn't know what I was doing last year, but this year I knew what to expect. To be leading, I didn't expect that at all.'
Davies, who matched the course record Wednesday with her 64, bogeyed four of her first five holes to tumble to minus-4. She started to reclaim those lost strokes with birdies at the seventh and ninth.
The Englishwoman moved back to minus-7 with a birdie at the 12th. Davies finally got back into red figures with an eagle at the par-5 closing hole.
'I was 4 over after five holes and considered heading off to the beer tent at that point. I could smell it from down there and I thought what would I rather do?,' Davies joked. 'But at the time I said to my caddie we were four off the lead, so it's not so bad. I know starting the day two shots ahead and all of a sudden we're behind, it wasn't good. But we had to build from there and we did. I made a fantastic putt at the last and now I'm just one off the lead, so it was a good turnaround.'
Sorenstam, a two-time winner here, birdied the first to get to minus-7. She wrapped short birdie putts at the fifth and seventh around a bogey at the sixth.
The Swede then birdied the ninth for the second time in two days. Sorenstam faltered to a three-putt bogey at the 11th. She regained that lost stroke and moved into a share of second place with a 16-foot birdie at the 16th. She parred the final two holes to close a round of 3-under 69.
'It was a pretty solid round. I had a lot of opportunities,' Sorenstam said. 'I hit a lot fairways and a lot of greens, but I hit every lip of the hole. I'm a little disappointed how I finished, but we have two more days to go.'
Catriona Matthew and Kim Saiki carded matching rounds of 5-under 67 to move into a tie for fifth at 7-under-par 137. They were joined there by Lorena Ochoa, who shot a 3-under 69. Lynnette Brooky and Rachel Teske are one stroke further back at minus-6.
Juli Inkster, the defending champion, struggled to a 1-over 73. She stands at 1-under-par 143 in a tie for 28th place.
Michelle Wie, the 14-year-old amateur, carded a 1-under 71 on Thursday and is tied for 26th place at minus-2.
With the invite-only group of 77 players participating, there is no cut at this event.