The Rams led most of the way but down the stretch Rivers and James combined for 12 points before Zoe Brooks added a layup. Rhode Island was 1 of 9 after Maye Toure's basket made it 56-63 with 5:17 to go.
Rivers scored 19 points with seven assists and seven steals and James had 17 points. Mimi Collins had 10 points and 11 rebounds for the Wolfpack (4-0) and Brooks scored 10.
Toure led the Rams (3-2) with 19 points and eight rebounds and Teisha Hyman had 12 points and nine boards.
N.C. State was unranked in the preseason poll but vaulted into the Top 25 by beating UConn last Sunday.
Rhode Island led by as many as 10 in the second quarter and it was 30-26 at the half as Sophie Phillips hit a late 3-pointer. She hit another 3 in the closing seconds of the third quarter to put the Rams up 48-46.
Rivers drilled a jumper to make it a one-point game and then James drove for a layup that finally put the Wolfpack on top for good at 57-56 with 3:38 to play. After two James free throws, Hyman pulled the Rams back within 59-58 at the 2:45 mark but James responded with a 3 and then N.C. State got breathing room with a three-point play by Rivers with 35 seconds to go.
Rhode Island was 4 of 17 behind the arc and made its only two free throws while the Wolfpack went 15 of 18 from the line.
NC State heads to the Virgin Islands and plays Kentucky on Thursday.
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