Al Horford added 16 points and 10 rebounds for the Hawks, who have won six of their last seven. Jamal Crawford had 15 points and Bibby finished with 13.
Vince Carter led the Magic with 18 points. Dwight Howard, back after missing two games with a stomach virus, contributed 14 points and 13 rebounds.
Orlando, which trailed by nine in the fourth, closed to 73-70 on Carter's three-point play with 40 seconds left. Bibby responded with a 3-pointer over Chris Duhon with 26.1 seconds remaining to help seal the victory.
Crawford scored six points in an 8-0 run to start the fourth quarter that put the Hawks up 62-55. Bibby's 3 with 2:45 left gave Atlanta its largest lead of the game at 71-62.
The Magic, who were missing point guard Jameer Nelson (stomach flu), rallied, but couldn't get a defensive stop when they needed it in the final minute.
Neither team scored more than 19 points or shot better than 38 percent in each of the first three periods. Smith, who also blocked four shots, dunked with 29 seconds left in the third to give Atlanta a 54-53 lead.
The Hawks led 36-34 at halftime, despite shooting 36 percent in the first two periods. Horford had 10 points and Smith added nine points and 11 rebounds, but the rest of the Hawks combined to hit only seven of 31 shots.
Orlando struggled even more, hitting just 12 of 37 shots (32 percent), including just 2 of 12 from 3-point range.
The Magic's only successful offensive stretch early on was sparked by a hustle play by Duhon late in the first quarter. Duhon dove two rows out of bounds to tip a pass to J.J. Redick, who finished the circus play with a layup at the other end.
Duhon got stuck in between the sideline seats and missed the next defensive possession altogether, returning in time to take an outlet pass from Bass and hit Redick for a 3-pointer on Orlando's next possession.
The impressive stretch was part of a 7-0 run that helped the Magic make up a nine-point deficit and pull even with the Hawks at 19-all through one.
NOTES: Three of the four Magic players who missed the last two games with stomach flu - Howard, Redick and Mickael Pietrus - played against Atlanta. ... Hawks G Maurice Evans, who shot 28 percent in three starts in place of the injured Joe Johnson, returned to a reserve role. ... The Magic had won seven of the last eight regular-season meetings with Atlanta and 11 of the last 12 overall, including a four-game sweep in the 2010 playoffs. ... Orlando lost for the first time in 12 games this season when giving up less than 90 points.