Chicago (8-2) led the entire contest. Jesse Meyer scored 10 of the Maroons' first 12 points as they jumped out to an early 12-2 lead.
The Maroons led 32-23 at halftime and built a 20-point advantage, 54-34, with 10:47 left in the contest.
A three-point basket from Drew Adams at the 9:21 mark gave Chicago its largest lead of the game, 61-34.
Hainje, who shared game-high scoring honors with Meyer and Brandon Woodhead, connected on four of five attempts from the field and was perfect on four free throw attempts.
Hainje became the first Chicago player this season to lead -- or share the team lead -- in points, rebounds, and assists in the same game.
Eleven different players scored as the Maroons won for the fourth time in five games at the Ratner Center.
Ray Byrns paced Cornell (4-5) with 11 points.
CORNELL (IOWA) (4-5) BYRNS, Ray 3-6 2-2 11; CODY, Tyler 4-14 0-1 9; LEWIS, Matt 3-3 0-0 6; LaDEW, Griffin 3-12 0-0 6; BITTER, Jeff 3-3 0-0 6; BECKER, Forrest 2-3 0-0 5; WALDEN, Ryan 1-2 2-4 4; GUNDERSON, Eric 1-2 0-0 2; NORTON, Adam 1-1 0-0 2; BORMANN, Brady 0-1 0-0 0; WOHRLEY, James 0-1 0-0 0; HANDKE, Chris 0-1 0-0 0; RATTRAY, Andre 0-2 0-0 0; TOMPKINS, Paul 0-4 0-0 0. Totals 21-55 4-7 51. CHICAGO (8-2) Hainje, Nate 4-5 4-4 13; Meyer, Jesse 4-11 2-2 13; Woodhead, Brandon 6-14 1-1 13; Adams, Drew 2-5 2-2 8; Brannon, Derek 3-5 0-0 7; Kowalewski, Marek 2-3 0-0 5; Pancratz, Jake 1-6 2-2 5; Watson, Tom 2-4 0-3 4; Kinsella, John 1-3 0-0 3; Sheline, Zach 1-1 0-0 3; Vismantas, Jason 1-3 0-0 2; Ellsworth, Kirk 0-0 0-0 0; Machones, Adam 0-2 0-0 0; Bonelli, John 0-0 0-0 0. Totals 27-62 11-14 76. Cornell (Iowa)................ 23 28 - 51 Chicago....................... 32 44 - 76 3-point goals-Cornell (Iowa) 5-22 (BYRNS, Ray 3-6; CODY, Tyler 1-5; BECKER, Forrest 1-1; GUNDERSON, Eric 0-1; TOMPKINS, Paul 0-3; LaDEW, Griffin 0-6), Chicago 11-32 (Meyer, Jesse 3-9; Adams, Drew 2-3; Brannon, Derek 1-2; Kinsella, John 1-3; Hainje, Nate 1-2; Sheline, Zach 1-1; Kowalewski, Marek 1-2; Pancratz, Jake 1-5; Machones, Adam 0-1; Woodhead, Brandon 0-4). Fouled out--Cornell (Iowa)-None, Chicago-None. Rebounds-Cornell (Iowa) 29 (WALDEN, Ryan 6), Chicago 41 (Hainje, Nate 8). Assists-Cornell (Iowa) 10 (LaDEW, Griffin 2; BYRNS, Ray 2; BITTER, Jeff 2), Chicago 18 (Hainje, Nate 6). Total fouls-Cornell (Iowa) 15, Chicago 11.