Three players did not complete their rounds as it was suspended due to darkness.
Thuhashini Selvaratnam and two-time winner Carol Semple Thompson share second place at 1-under-par 71. Mary Ann Lapointe and Kerry Postillion are one stroke further back at even-par 72 at Shadow Hawk Golf Club.
Woodard, who got into the championship by winning the last spot at her sectional qualifying site in a three-way, sudden-death playoff, played the front nine in 1 under after a birdie on the second.
The 31-year-old from Tennessee ended a string of 11 straight pars with a birdie on the par-5 14th. She made it two straight with a birdie on 15. Woodard finished with a birdie on the par-5 closing hole to cap her round of 68.
That 68 set a new Women's Mid-Amateur scoring record by one stroke.
'How about that,' Woodard said about setting the new record. 'I missed three fairways, but not by much, so I was never in the deep rough. When I missed a green, it was only by a couple of inches.'
Ivy Steinberg, Wallace Hamerton, Mari Miezwa, Lori Planos and Martha Lang share sixth place at 1-over-par 73. Kay Daniel, Daria Cummings, Kathy Hartwiger and Laura Coble are one stroke further back at plus-2.
Corey Weworski, the defending champion, is among eight players tied for 15th at 3-over-par 75.
After Sunday's second round of stroke play, the field will be cut to the low 64 players, who will advance to match play.