Garrard (3-14) was outshot 33-7 by the Lady Scotties, who led 2-0 at halftime.
Rachel Keller started the scoring for Mercer with 18:00 left in the first half, and Goodman got her first goal with 12:55 left.
Abby Parsons scored Garrard's only goal off a throw-in from Tiffany Asberry with 37:30 to play to open the second-half scoring.
Goodman scored with 33:00 left and again with 8:00 left on a header off Julianne White's pass. Between those goals, Cala Alford's corner kick deflected off a Garrard player for an own-goal with 18:00 left.
Danville 2, Berea 2 - At Berea, Miguel Magana scored two goals after Danville (5-7-1) fell behind 2-0 to help the Admirals salvage a tie against Berea (6-4-2).
Magana scored with 16:53 left in the first half off a free kick, then scored his 14th goal of the season on a free kick off Miles Garriott's assist with 8:46 left in the half.
"We're mighty proud of the way he's playing," Danville coach Gary Reynolds said. "(We) came out very flat and sluggish. It took us a while to sort things out, but when Miguel scored the first goal it kind of pepped us up a little bit.
"We got down early and we came back, and that shows something about my guys and how they play."
The Admirals might have fallen behind 3-0 had Matt Booth not made what Reynolds said was "a tremendous save" on a penalty kick between Berea's two goals.
Reynolds said Danville, which outshot Berea 15-8, controlled the ball for much of the scoreless second half.
"We possessed the ball and took plenty of shots, just weren't sinking any," Reynolds said.
Russell County 2, Lincoln County 2 - At Stanford, Drew Terry had a goal and an assist as Lincoln (1-9-1) tied Russell (1-12-1).
Terry assisted on a goal by Justin Kolasa, then scored off an assist by Daniel Reyes.
"The kids passed the ball better than they ever had," Lincoln coach Lindsey Thurman said. "We probably had 20 or 30 more shots on goal than our opponent, but we ended up with a tie."
Sayre 4, Boyle County 1 - At Lexington, playing without two starters, Boyle (8-4-1) fell behind 2-0 in the first half and could never catch Sayre (4-4-3).
"In the second half we played much better and seemed to move the ball around a lot better," Boyle coach Greg Conley said.
Patrick Morgan scored Boyle's only goal off an assist from Eric Curtis.
Ben McClain made his first start in goal and Patrick Barsotti made his first start on defense.