The loss was just the third in the past 13 games for the Rams.
Aaron Jackson added 17 points for the Dukes who shot .528.
There were 13 ties and seven lead changes before Bill Clark drilled a 3-pointer that gave the Dukes a 72-69 lead with 3:31 left. Jackson broke Norm Nixon's school record with his 179th assist of the season on the play.
Duquesne upped its lead to five on a pair of Aaron Jackson free throws with 2:18 on the clock before Baron cut it to two with a 3-pointer with 32 seconds left. Jason Duty hit a pair of free throws with 25 seconds remaining to seal the victory.
Duquesne briefly led by seven early in the second half, while Rhode Island's largest lead was two on a number of occasions.
DU outscored URI 32-30 in the paint despite being outrebounded 43-29. The Dukes went 10-of-24 from the 3-point arc with five different players converting at least once.
Rhode Island finished 8-of-23 from the arc with Baron accounting for all eight field goals.
- The victory clinched DU's first 20-win season since 1981 (20-10) and second since 1972 (20-5)
- It marked the first time Duquesne won two A-10 Championship games since 1985 when the No. 8 Dukes defeated No. 9 Penn State and No. 1 West Virginia before losing to No. 4 Rutgers in the semifinal at Piscataway, N.J.
- This was Duquesne's first win over Rhode Island under Ron Everhart, leaving Richmond is the only A-10 team DU has yet to defeat since Everhart took over at Duquesne prior to the 2006-07 season