Reggie Johnson scored 16 points on 7-of-9 shooting for Miami (15-10, 4-7), which was bidding for its first four-game ACC winning streak since February 2008. The Hurricanes fell to 1-17 since 2000 against teams ranked in the AP Top 25, the lone win coming against Duke three seasons ago.
The Blue Devils didn't let that happen again, building a double-digit lead midway through the second half and controlling the game from there.
Miami got within six points twice in the final minute, only to have Tyler Thornton hit two free throws on ensuing Duke possessions to keep the Hurricanes out of reach.
In short, when Smith got rolling, everything started to click for Duke.
He went to the bench with two fouls - and a bigger problem - with 13:08 left in the opening half.
After fouling Johnson, Smith was inadvertently poked in the eye, then was dealing with some vision and light-sensitivity issues on the Blue Devils' bench, where he remained for nearly 9 minutes. It was an opportunity missed for Miami.
The Hurricanes were down 16-15 when Smith left the game, and the deficit was 31-27 when he returned, in part because Miami's best scorer was on the bench as well. Grant scored 12 points and hit three 3-pointers in the first 6:53 of the game, then sat out the final 9:32 until halftime after getting his second foul. Smith didn't make his first field goal until 15:16 remained in the game, a pull-up in transition. Once he started, the scores came in bunches. He made three more shots in the next 3 minutes, capped by a driving layup after Julian Gamble missed a dunk at the other end to give Duke what was then its biggest lead, 61-51 with 11:34 remaining.
Duke hadn't played since Wednesday's 79-73 home win over North Carolina, a game in which the Blue Devils fought their way back from an early 16-point deficit.
They started slowly Sunday as well. Miami made its first four shots, capped by Grant connecting on a 3-pointer while getting fouled by Smith for a quick 10-4 lead.
Things calmed down quickly.
Duke scored the next seven points, and although Miami reclaimed the lead six more times during a back-and-forth first half, the Hurricanes' biggest edge came at 37-33 after Rion Brown made a 3-pointer with 2:46 left.
Duke closed the half on a 9-0 run, and after Miami got within one early in the second half, another 9-0 burst - fueled when Smith finally found his scoring groove - pushed the Blue Devils' lead back to double digits.
The Blue Devils tightened up their defense in the second half as well, holding Miami to 41 percent from the floor in the final 20 minutes.