Woodard, who earned medalist honors by three shots on Sunday, eased to a 5 and 4 victory over Leslie Folsom at Old Waverly Golf Club. She will next face Marilyn Hardy, who was a 3 and 2 winner over Rebecca Gard on Monday.
Seven-time USGA champion Carol Semple Thompson also advanced to the second round of match play following a 1-up win over Nancy Fitzgerald.
Semple Thompson, who owns two Women's Mid-Amateur titles among her seven USGA championships, moved on to face Marianne Towersey, a 2 and 1 winner over Alicia Kapheim in the first round.
The two other past Mid-Am champions remaining in the field also advanced, as Virginia Grimes rolled to a 7 and 5 win over Barbara Byrnes and Ellen Port squeezed past Donna Gonsalves, 1-up.
The remaining winners Monday were: Vicky Vandenbrook, Michelle Griffith, Meghan Bolger, Tara Joy-Connelly, Lori Planos, Tracy Welch, Benedikte Brynestad Grotvedt, Sydney Moore, Jill Hardy, Joan Higgins, Mina Hardin, Lisa Smego, Robin Burke, Rheba Mabie, Laura Coble, Tanna Lee Richard, Thuhashini Selvaratnam, Martha Leach, Erin Packer, Suzi Spotleson, Kelly Schaub, Ann Pohira, Mari Mieswa, Diane Lang, Lea Venable and Lynn Thompson.