Lanning narrowly missed out on her maiden Test century on a big opening day in Canberra, but still peeled off the biggest score by an Australian captain in a home Ashes Test.
After coming to the wicket at 3-43, Lanning's 93 helped Australia steady the ship and then emerge on top as part of a 169-run stand with Haynes.
Haynes also fell just short of her first Test century, watching Australia lose their first two wickets for just three runs before finishing on 86 herself.
"It was never really a panic," Haynes said.
"Meg and I just spoke about leaving with good intent. So still looking to score but getting the bowlers to come to us a little bit more."
Ashleigh Gardner also hit a quickfire 56 late, while a wild shot from Tahlia McGrath on the final ball of the day left her caught behind on 56.
But still, Australia have the firm advantage at Manuka Oval with the hosts already leading the multi-format series 4-2.
No team has ever been beaten in the 142 women's Tests played when they have scored in excess of 300 in the opening innings.
That figure is helped by the fact that matches are only given four days, with a significant number ending in draws.
A win for Australia in Canberra will ensure they wrap up the Ashes, while a draw would mean they only need to win one of the three ensuing ODIs to retain the trophy.
And if Australia do keep the Ashes for a fourth straight series, they will have Haynes and Lanning to thank.
When Alyssa Healy (0), Beth Mooney (3) and Ellyse Perry (18) fell early, Katherine Brunt (3-52) and Nat Sciver (3-41) looked as if they had put England back in the series.
But after hitting an unbeaten 64 in Australia's series-opening Twenty20 win, Lanning cut beautifully on Thursday and hit the ball nicely through the offside.
It came as England often bowled too short and wide, with Haynes also making use of any width in the highest score by an Australian opener this century.
She also did it in what she concedes could likely be her last Ashes Test, at age 35 and the next one still 18 months away.
England missed crucial chances, including two when Lanning was on zero and 14 in the slips that would have swung the game.
Australia's skipper also survived a shout for both lbw and caught behind, while another ball appeared to brush her bat but England did not appeal.
Haynes was also put down, on 44, before the pair both fell within three balls of each other after tea and made way for the Gardner and McGrath counterpunch.
"All the bowlers can do is create them. We have to take them really," Sciver said.
"We're frustrated with the drops and maybe we lacked a bit of lack of energy in the middle session."
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