The Cougars are now 6-2 overall after dropping the early game of the day to No. 2-ranked Auburn 8-1.
SIUE returns to action Saturday morning at 10:30 against Mercer.
"We were able to get it done offensively, and Haley got it done in the circle," said SIUE Head Coach Sandy Montgomery of the Evansville victory.
Chambers improved to 4-1 with a 14-strikeout effort. The senior already has three starts with more than 10 strikeouts this season.
Evansville struggled defensively with six errors, but it was the Cougar offense that took charge with nine hits overall, including two each from Chambers-Book, Schafer, Reagan Curtis and Conner Cutright.
"We hit the ball awfully hard," added Montgomery.
SIUE took the lead for good in the third inning against Evansville with back-to-back RBIs from Allison Smiley and Schafer.
Schafer picked up her second RBI of the game with a single to left in the fifth inning. Curtis added an RBI double down the left field line in the sixth. Chambers-Book provided insurance with a two-run single in the seventh.
Against Auburn, the Tigers used a pair of big innings to push past the Cougars. Auburn didn't score until the third inning yet rallied for four runs.
Emily Ingles went the distance and yielded eight hits to the defending national runner-up. She is now 1-1.
Chambers-Book provided the Cougars' lone RBI in the sixth.
"They (Auburn) had two big innings," said Montgomery. "Emily had some really good innings today, but we made some mistakes. Teams like that are going to capitalize on that."
Schafer said that the Cougars played well in getting back on the winning track.
"Our leadership is incredible," she said. "The seniors have been awesome in incorporating all of us."