Acting captain Matt Prior produced a sparkling unbeaten 133, but Sussex were let down by their fragile top order as they were bowled out for 212 with Harmison taking 4-75 and Callum Thorp 4-77.
That left Durham only 126 to win and Michael Di Venuto set them up with a hard-hitting 60 after Jason Lowry struck early on to remove Phil Mustard for a duck and first-innings centurion Will Smith for nine.
Former Sussex batsman Di Venuto failed with 22 needed when his miscued an attempted pull off Luke Wright. But Neil McKenzie (41 not out) and skipper Dale Benkenstein eased Durham home with a day to spare as the title holders suffered their first defeat at home in the championship since the last game of the 2004 season.
Fine centuries from skipper Dale Benkenstein and Will Smith saw Durham recover from 11 for four to post 301 and gain a valuable first-innings lead of 87 over Sussex. Benkenstein and Smith added a superb 205 in 49 overs for the fifth wicket at Hove before a patient 34 from Ben Harmison helped Durham to a third batting point.
Former West Indies seamer Corey Collymore finished with 4-51 and left-armer Jason Lewry took 4-56 for Sussex, who were quickly in trouble when they batted again. The defending champions – unbeaten at home in the championship since the last match of the 2002 season – lost openers Chris Nash and Carl Hopkinson by the close in struggling to 15 for two, still 72 behind.
England fast bowler Steve Harmison shrugged off a slight foot injury to have Nash caught behind, and Harmison later had Michael Yardy dropped at short-leg before Callum Thorp bowled Hopkinson. Durham, resuming the second day on a rocky 10 for three, made the worst possible start with Collymore picking up his third wicket without addition.
The 30-year-old struck in his first over, and the second of the day, by having Neil McKenzie caught behind off a faint edge pushing only half forward.
But captain Benkenstein then joined Smith to frustrate the defending champions with an enterprising stand to turn around Durham’s fortunes on a pitch that became increasingly flatter. Ben and Steve Harmison combined to score 34 and give Durham a third batting point.