ACC rookie of the year Jabari Parker scored 18 points and Hood had 17 for the third-seeded Blue Devils (25-7).
They blew a 13-point lead with 12 minutes left before regrouping just in time to avoid joining No. 15 North Carolina and No. 11 Syracuse as ACC quarterfinal losers. Duke will play seventh-seeded North Carolina State in a semifinal Saturday.
Rod Hall scored 13 points to lead sixth-seeded Clemson (20-12), and his runner in the lane with 7.4 seconds left capped a late 15-5 run and gave the Tigers their only lead of the second half at 62-61.
After Hood's free throws, Hall made it deep into the lane before he was stripped by Tyler Thornton a moment before the buzzer sounded.
Clemson coach Brad Brownell and the rest of the Tigers' staff erupted when no foul was called.
They lost their first ACC tournament game here last year to Maryland and before that were memorably upset by 15th-seeded Lehigh in their NCAA tournament opener in 2012.
Damarcus Harrison and Hall hit back-to-back 3s to start the burst in which the Tigers scored on seven straight possessions.
McDaniels hit a free throw with 47.7 seconds left to pull Clemson to 61-60. When Sulaimon missed a floater with about 15 seconds left, Landry Nnoko pulled down the rebound and kicked it out to Hall -- who hurried downcourt and hit his runner in the lane to briefly put the Tigers ahead.
Hood then flew right back the other way, drew contact from McDaniels while attacking the basket and hit both ends of a one-and-one for the game's final points.
Nnoko finished with 10 points for Clemson, which won the only regular-season meeting -- a 72-59 romp in January that dropped Duke to 1-2 in the league and caused a significant amount of soul-searching among the Blue Devils.
The Tigers shot 67 percent in the second half of this one and the only defensive stop the Blue Devils got in the final 5 minutes was the one by Thornton that decided the game.