Mathias scored 15 of his 18 points in the first half and Vince Edwards added 11 of his 14.
"With our experience and our seniors, we know the offense pretty well," Mathias said. "We were taking some rushed shots and forcing some things. We just settled in after the first media timeout."
Mathias finished 5 of 8 from the field and 6 of 6 from the free throw line to go with four rebounds and three assists.
Purdue finished 36 of 61 from the field (59 percent), including 9 of 19 from 3-point range.
Coach Matt Painter liked his team's effort, but did not like being out-rebounded 40-39.
"When you shoot almost 60 percent, you are going to win the basketball game," Painter said. "But they got 19 more shots in the first half than we did, which is alarming."
The Boilermakers outscored the Cougars 24-2 from the free throw line.
"When you are not shooting for a little bit, you have to get something going, so getting to the free throw line is a big thing," Mathias said. "Once you notice they are in the bonus, you try to be more aggressive. It definitely is something you are conscious of."
Painter also liked the play of freshman point Nojel Eastern.
"Nojel was great," Painter said. "Before he entered the game, our ball movement was lackluster."
The visiting Cougars (0-1) jumped to a 10-5 lead with 16:04 remaining in the first half before the Boilermakers countered with a 17-4 run to lead 24-14 at the 10:24 mark.
Purdue (1-0) was celebrating its 50th season in Mackey Arena and unveiled the 2017 Big Ten championship banner before tipoff.
Sophomore guard Carsen Edwards and center Isaac Haas added 16 apiece for Purdue.
Center Julian Torres scored 20 points and guard Daniel Kinchen had 17 for SIU-Edwardsville.
The Boilermakers shot a blistering 59 percent (16 of 27) before intermission to build a 52-32 lead through 20 minutes and were never threatened.
Purdue improved to 12-1 openers in season openers for Painter. The Boilermakers improved their lead to 80-57 with 9:39 remaining.
NOTES: SIU-Edwardsville assistant coach Tarrance Crump is a 2008 Purdue graduate who played for coach Matt Painter, scoring 338 points in 67 career games. ... The Cougars are in their 50th season of basketball. Third-year coach James Harris is 12-47 after Friday's loss. ... Purdue is 1,766-1,003 in 120 seasons of college basketball. ...The Boilermakers have won eight consecutive games in Mackey. ... Before playing the Cougars, Purdue's past four season-opening victories were by 40, 41 and 44 and 31 points. ... The Boilermakers are coming off a season in which they averaged 8.7 made 3-pointers, 45th best in the nation.