Kyle Singler added 15 points and scored his 2,000th career point during a game-opening 26-4 run that took the drama out of this one early. The Blue Devils (14-0) never let the Blazers (10-3) closer than 14 points the rest of the way.
Duke has won 24 straight games dating back to last season's run to the Atlantic Coast Conference and NCAA tournament championships, and 32 of 33 overall.
Jamarr Sanders scored 21 points to lead UAB, including a 3-pointer on the game's first possession. But that lead lasted just 31 seconds, as Blue Devils answered with 16 straight points to blow the game open.
Duke has won all but two games by double-digit margins as it heads into the heart of its ACC schedule. The Blue Devils face Maryland at Cameron Indoor Stadium on Sunday, and still have one more nonconference game against Temple here in late February.
The Blue Devils are still waiting to learn when - or if - star freshman point guard Kyrie Irving will be back, but Smith has more than filled in at the helm of the offense.
He had 10 points during Duke's 16-0 run, making a pair of 3s in the first 4 minutes before driving past Aaron Johnson for an easy layup to cap the spurt.
It was just the start of another huge performance for the senior while Irving sits out indefinitely with an injured right big toe. Smith had 20 points in the first half, then hit a free throw with 9:36 left to tie his previous career high of 29 set against Baylor in last year's NCAA regional final.
He certainly scored his personal-record basket in style, blowing past a defender near the 3-point arc and soaring into the lane for an emphatic one-handed dunk to make it 76-56 with 5:55 left.
Smith finished 11 for 22 from the field to go with seven rebounds and five assists. He's scored at least 22 points in five straight games.