Woad, expected to make her Team Europe debut in this September's Solheim Cup, charged top of the leaderboard after following a second-round 64 with a five-under 65 during a weather-disrupted third round at Maketewah Country Club.
The world No 10 sits on 11 under and with a commanding lead over American Amanda Doherty, with Haeran Ryu four strokes back in third spot ahead of three-time major champion Lydia Ko.
- Kroger Queen City Championship: Latest scores
- Got Sky? Watch golf and more LIVE on your phone
- Not got Sky? Get Sky Sports or stream no contract
Jeeno Thitikul is part of the logjam on five under also containing Rose Zhang, while world No 1 Nelly Korda and overnight co-leader Jin Young Ko slipped to tied-19th and nine strokes back after rounds of 72 and 75 respectively.
Defending champion Charley Hull was two off the lead after the opening day but fell to three over for the tournament after registering just one birdie - and carding three consecutive bogeys - in a three-over 73.
How Woad moved ahead in Ohio
Woad birdied the par-four third and posted back-to-back gains from the seventh, then cancelled out a bogey at the par-three ninth by starting her back nine with successive birdies.
She took advantage of the par-five 14th and added her seventh birdie of the day at the 16th, taking her to 12 under, with Woad's lead over Doherty cut to three strokes after a penultimate-hole bogey.
"I just tried to take last week as a bit of an anomaly," said Woad, who missed the cut at last week's Mizuho Americas Open. "I been playing pretty solid before then, consistently, but that course was a bit funky in places, so I just tried to ignore it.
"Didn't putt very well last week and turns out my putter grip wasn't on straight, so got a new putter grip on. I was putting really bad so I was obviously trying to look for an excuse that wasn't me - it was the grip.
"I just hit a lot of fairways and greens the past two days. Day one I didn't hit as many fairways. I think if you do that [fairway], you do have lot of chances around here."
Forsterling moves two ahead at Amundi German Masters
On the Ladies European Tour, Alexandra Forsterling's brilliant birdie burst helped her take a two-shot lead into the final round of the Amundi German Masters.
The German posted four consecutive birdies from the 12th on her way to a four-under 69, lifting her to 10 under despite taking advantage of the two par-fives over the closing three holes.
A level-par 73 dropped halfway leader Sara Kouskova to tied-second alongside Chiara Noja, with German's Leonie Harm four off the pace in a share of fourth alongside Canada's Anna Huang.
Esther Henseleit slipped five behind after two double-bogeys in her four-over 77, with England's Esme Hamilton heading into the final day tied-eighth after a one-over 74 dropped her to four under.
The Amundi German Masters is live on Sunday from midday on Sky Sports Golf, with the Kroger Queen City Championship live on Sky Sports Mix from 8pm. Get Sky Sports or stream with no contract.
