Jlynn Counter's driving layup with eight minutes to go put IUPUI on top 65-64, but Davis answered with a 3-pointer to start a 14-0 run that put the Titans in charge.
Davis added a stepback jumper and another 3, then A.J. Oliver had a 3-pointer before Anderson capped the run with yet another from beyond the arc, making it 75-65 with 3:14 to go.
Counter had 23 points, five rebounds and 5 assists for the Jaguars (3-18, 0-10). DJ Jackson added 17, John Egbuta 13 and Vince Brady II and Chris Osten 12 each.
Davis had 25 points in the first half, his 94th career 20-point game, as Detroit Mercy took a 39-38 lead.
The Jaguars, who have lost eight straight, shot 56% in the first half, and 54% in the second but couldn't keep pace with the Titans, who shot 61% in the second half. Detroit Mercy was 8 of 13 from 3-point range after the break after going 8 of 20 in the first half.
Davis, who leads the nation in scoring at better than 26 points a game, has 12 regular-season games remaining. He has five 40-point games and 32 30-point games in his career.
The Titans are home Monday against Oakland.
More AP college basketball: https://apnews.com/hub/college-basketball and https://apnews.com/hub/ap-top-25-college-basketball-poll and https://twitter.com/AP_Top25