Division One champions Durham ended their season with a defeat as Sussex's six-wicket victory at Hove clinched third place in the table.
Chris Nash scored 108 as the hosts chased down a target of 295 after Durham's second innings of 458 had brought them right back into the game.
Nash's opening partner Luke Wells made 88, meaning he fell six runs short of lodging 1,000 first-class runs for the season, but the knock still helped lay the foundations for Sussex's highest finish since they won the title in 2007
Sussex made relatively light work of what looked a tricky run chase, Nash and Wells putting on 163 for the first wicket before Wells edged Graham Onions to slip, where Paul Collingwood took a fine catch.
But Nash and skipper Ed Joyce shared a second-wicket stand of 80 in 17 overs during which Joyce moved into fourth among the leading run-scorers this season.
Borthwick eventually had Nash caught at long-off for 108 and with the game all but lost Collingwood threw the ball to wicketkeeper Phil Mustard, who claimed his maiden first-class wicket with his fifth ball when Luke Wright (13) was trapped lbw.
Earlier, Matt Prior (6) had fallen to the part-time spin of Smith but there were still 10 overs left when Brown hit the winning boundary, while Joyce finished on 65 not out.
Earlier, Usman Arshad made his highest first-class score as Durham, who had been 120-6, were finally bowled out for 458.
Arshad hit 83 off 88 balls with 12 fours and three sixes before he was brilliantly caught by Joyce at short mid-wicket when a drive struck him on the arm and he held onto the rebound.
Arshad had added 106 in 21 overs for the eighth wicket with Keaton Jennings (127) before the opener was caught behind cutting at Nash. He had batted for more than seven hours and faced 308 balls.