Jon Scheyer scored 23 points, and Singler finished with 21 points for the Blue Devils (3-0), who fell behind by 12 early and trailed for most of the way.
Singler twice hit a pair of foul shots in the final minute to put the Blue Devils up by one, before Rhode Island (1-1) called time out with 10.6 seconds left and worked the ball to Jimmy Baron. With Singler in his face, his fallaway jumper glanced off the rim, clipped a Rams player and went out of bounds with 4.9 seconds on the clock.
Scheyer made two free throws with 3.7 seconds left, and Baron's half-court heave bounced off the glass as time expired to seal Duke's NCAA-best 62nd straight nonconference home win at Cameron Indoor Stadium.
Baron scored 21 of his 24 points in the second half and matched a career-high with eight threes.
No. 6 Michigan State 100, Idaho 62: : Chris Allen scored a career-high 21, leading host Michigan State (1-0) over Idaho (1-1).
No. 9 Notre Dame 94, South Carolina-Upstate 58: : Luke Harangody had 30 points and 14 rebounds to lead host Notre Dame (1-0) over South Carolina-Upstate (0-2).
No. 19 Florida 81, Bradley 58: : Dan Werner and Walter Hodge each scored 17 to lead the host Gators (2-0) past the Braves (1-1).
No. 19 Baylor 81, No. 2 Stanford 65: : Rachel Allison scored 25 points and Jhasmin Player added 14 to help the host Bears (2-0) to an upset of the Cardinal (1-1). It marked the highest ranked opponent that Baylor has beaten in the regular season.
No. 6 North Carolina 77, Virginia Commonweath 65: : Rashanda McCants scored 15 points to help host North Carolina (2-0) overcome a slow start and beat Virginia Commonwealth (1-1) in the second round of the Women's Preseason National Invitation Tournament.
No. 8 Duke 98, Maine 31: : Chante Black scored 16 points and reached 1,000 for her career as the host Blue Devils (2-0) routed the Black Bears (0-1).
No. 9 California 67, Nevada 53: : Ashley Walker scored 27 points to surpass the 1,500 mark for her career and also grabbed 17 rebounds, leading host California past Nevada.
No. 11 Texas A&M; 56, Pittsburgh 50: : Tyra White scored 13 points to help Texas A&M; (2-0) beat Pittsburgh (0-1) in the State Farm Women's Tip-Off Classic in Baton Rouge, La.
No. 12 Vanderbilt 90, Western Kentucky 72: : Christina Wirth scored 24 points to lead visiting Vanderbilt (2-0) to a rout of Western Kentucky (1-1).
No. 13 Texas 110, Saint Mary's (Calif.) 76: : Erika Arriaran scored 21 points to lead Texas to a win over Saint Mary's in the second round of the World Vision Classic in Austin, Texas.
No. 16 Notre Dame 62, No. 24 LSU 53: : Ashley Barlow scored 10 of her 19 points during a run to start the second half and visiting Fighting Irish (1-0) beat the Tigers (0-1).
No. 17 Arizona State 86, Tulane 53: : Dymond Simon scored 15 points to help host Arizona State (2-0) cruise to a victory over Tulane (1-1) in the second round of the WNIT.
No. 18 Ohio State 92, Army 58: : Jantel Lavender scored 28 points to lead the host Buckeyes (2-0) past the Black Knights (0-2).
No. 21 Florida State 81, Florida Gulf Coast 62:: Tanae Davis-Cain and Jacinta Monroe combined for 33 points as the host Seminoles (1-0) turned back a furious rally by the Eagles (1-1).
No. 22 Xavier 62, Indiana 59: : Jerii Taylor scored 15 points to lead visiting Xavier (2-0) to a win over Indiana (1-1).
No. 23 Purdue 80, Indiana-Purdue Indianapolis 44: : Lindsay Wisdom-Hylton had 16 points and 11 rebounds to help host Boilermakers (1-0) beat Jaguars (1-1).
No. 25 Old Dominion 70, Dayton 58: : Jessica Canady scored 23 points and Old Dominion (2-0) beat Dayton (0-2) in the World Vision Classic.