Davidson (20-6, 11-4) and Rhode Island (19-7, 11-4) are now tied with Virginia Commonwealth and Dayton atop the Atlantic 10 Conference. No. 22 VCU lost to Richmond in double overtime and Dayton earned a share of first with a win over George Mason.
The Rams held a 58-54 lead going into the final minute, but Tyler Kalinoski converted a three-point play with :51 left to pull Davidson within one, 58-57. Hassan Martin converted the first of two free throws to push the lead back to two before Gibbs drilled the game-winner. Rhode Island's Jared Terrell missed a 3 with :02 left and Davidson grabbed the rebound to end the game.
Kalinoski finished with 21 points to lead the Wildcats to their 20th win and Gibbs finished with 15 points.
Martin finished with 17 points and E.C. Matthews added 16 to lead Rhode Island.