Adams hit the 1,000-point mark at 3:29 mark of the third quarter.
"In the first half I was not making my free throws, it was stressful," said Adams. "But my teammates told me to keep my focus and not worry about it. After I hit it, I feel like it gave us momentum as a team."
"I was proud of Gwen getting into the 1,000-point club," said SIUE Head Coach Paula Buscher, whose team improved to 1-0 in the OVC and 4-8 overall. "We have had two of them get it this year (also Donshel Beck). It's one of those great individual accomplishments, and it's even better when you come out with the win."
SIUE's defense was front and center in the OVC opener, holding Austin Peay to 27.9 percent shooting for the game (12-43).
It also was the lowest point total SIUE has allowed to an opponent in any OVC game since joining the league. The previous low was 39 against Jacksonville State in SIUE's first OVC game Dec. 31, 2011.
"It was good to open up with a win," said Buscher. "Now we have to enjoy it tonight, regroup tomorrow and get back to work."
Buscher credited SIUE's team communication for the strong defensive effort.
"I thought they did a great job with that," said Buscher. "All in all, our defense was rock solid."
SIUE's offense shot 19 of 43 from the field (44.2 percent) for the game. Lauren White led all scorers with 16 points. Beck added 13.
The Cougars opened the game with a slim 13-9 lead after the first period on 5-of-9 shooting from the field. Neither team presented much offense in the second quarter although the Cougars outscored the Governors 8-7 in the period.
Buscher said she challenged her team to keep up its defensive pressure and set the tone for the second half.
The Cougars did so by pushing the lead to double digits at the 4:55 mark of the third period on a jumper by White.
SIUE turned up the offense with the first nine points of the fourth quarter on a three-pointer by White, two baskets by Beck and a layup by Zaria Whitlock, pushing the lead to 51-30 with 7:49 to play.
Falon Baker, who tossed in nine points, was the leading scorer for Austin Peay, now 7-5 overall and 0-1 in the OVC.
The Cougars also dominated the boards 38-18 yet turned the ball over 26 times.
"We have to sharpen up our game," admitted Buscher. "But I give our team a lot of credit. I was very happy with the last 20 minutes."
SIUE continues OVC play Saturday with a 5 p.m. contest at Murray State.