St. Thomas stayed one-half game behind first-place Gustavus (12-2), a 73-66 winner at Carleton.
The Tommies outrebounded Augsburg 46-19 and shot 55% from the field. (29-of-53). The Toms also made 22-of-26 foul shots as they improved to 6-1 at home this season.
Peterson's 18 points were his second most of the season. Anderson sank five 3-pointers.
For UST, sophomore center Isaac Rosefelt had 14 points and 12 rebounds; Alex Weaver had 13 points; and Sean Sweeney had eight assists in 21 minutes.
UST used a 12-0 run to build a 26-10 advantage and led 42-26 at halftime. The Toms built the lead to 39 points with 7:00 to play as they swept the season series and won their eighth in a row vs. Augsburg.
Senior Lucas Olson-Patterson had 24 points and Justin Kozlowski had 12 points for the Auggies, who lost their sixth in a row.