SIUE, now 39-11, advances to play second-seeded UT Martin, which defeated Tennessee Tech 1-0 in its opening game. Game time is 12:30 p.m. Thursday.
Eby took the first pitch over the fence in left-center field. She only made it to the batter's box because Talisa Morton reached on a two-out infield error.
"Coach (Sandy Montgomery) actually gave me a hit and run, which is my favorite thing to get because I can just hit the crap out of the ball," said Eby.
Eastern Kentucky, 25-30, got started quick with a run in the first inning. Rachel Minogue doubled to the gap in left center, driving home Krislyn Campos.
"You have to give credit to EKU," said Montgomery. "They came out ready to play and gave us all we wanted."
SIUE tied the game in the third inning. Reagan Curtis singled past the shortstop for the first of SIUE's three hits for the game. Jane Smith pinch ran for Curtis and would score for the 25th time this season in 46 appearances. She eventually moved to third and scored on a sacrifice fly by Alyssa Heren.
Montgomery said she was happy with how the Cougars dealt with being down early.
"We were not as sharp as we needed to be," said Montgomery. "The kids were poised and mature. They handled the adversity of the game and the crowd. It was a nice win for us."
After Eby's homer in the fifth, Haley Chambers-Book added another run with a solo blast to right field off EKU pitcher Mollie Paulick in the sixth inning.
Chambers-Book collected the win, her 25th of the season. She allowed three hits and struck out seven, lowering her season earned run average to 1.18.
Montgomery said the Cougars will get ready for its next round game.
"Everybody is ready to play," she said. "There is a lot of intensity and a lot of competitive spirit."