McDermott became the 64th player in NCAA history to score more than 2,500 career points, and he extended his streak of consecutive free throws made to a Creighton-record 39.
The Bluejays (10-2) made a season-high 16 3-pointers and carry a five-game win streak into their Big East opener against Marquette at home Tuesday night. Jahenns Manigat matched his career high with five 3s and Wragge also made five. They each scored 15 points.
Clarke Rosenberg had 14 points, Quinton Pippen had 13 and Matt Ross added 11 for the Cougars (5-8), who have lost all eight of their road games by an average of 21 points.
McDermott has scored at least 20 points in all but one game this season and in 18 of 20. The two-time first-team All-American increased his career points total to 2,513.
Wragge's four 3-pointers in a row came during an 18-3 run that put Creighton up 66-44. Until the game-turning spurt, the Bluejays got more than they expected from a Cougars team picked sixth in the nine-team Western Athletic Conference.
McDermott scored 16 points in the first six minutes against the Cougars. He made his first four 3-pointers, and when his fifth attempt rattled in and out, the CenturyLink Center crowd of 17,466 let out a collective sigh.
McDermott couldn't regain his mojo after taking a three-minute breather. Pippen, who gives up 4 inches to the 6-foot-8 McDermott, denied him the ball in the post, and he couldn't get freed up for looks on the perimeter.
Aside from a desperation shot that missed at the buzzer, McDermott attempted only one shot over the last 12 minutes of the half. Before McDermott's twisting drive to the hoop early in the second half, he went 18 minutes between field goals.
Creighton's McDermott-fueled surge to start the game created a 12-point deficit for the Cougars. But Pippen's third 3-pointer in a row cut it to 27-26. While the Cougars clawed back, the Bluejays went 6 1/2 minutes without a field goal.
Manigat ended the drought with a 3-pointer, and Grant Gibbs and Manigat made two more from beyond the arc as the Bluejays went out to a 45-38 halftime lead.
McDermott went to the line for the free-throw record after Johnny Griffin fouled him with 10:22 to play. He swished both, running his streak to 37 in a row. Booker Woodfox had set the record of 36 straight in the 2008-09 season.
Creighton hasn't trailed in its last four home games. The last time the Bluejays were behind at home was late in the first half of a Nov. 23 game against Tulsa - a stretch of more than 180 minutes.
Chicago State made 10 of 24 3-pointers but shot just 38 percent overall. Eight of Creighton's opponents have shot under 40 percent.
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