O'Neill took 3-35 in Durham's second innings as the visitors were dismissed in mid-afternoon on the fourth and final day leaving Notts requiring 89 to win, which they knocked off in 17.1 overs.
The Sheffield Shield's player of the season wrapped the Durham innings with a neat caught-and-bowled of England seamer Matty Potts.
But the day belonged to Ashes hopeful Josh Tongue who took 5-66 with Dillon Pennington, another on the fringe of England selection, chipping in with 2-61.
Tongue, who missed all of 2024 with injury, making his comeback with England Lions in Australia in January, took four of his wickets with an 80-over old ball as Durham collapsed from 5-268 to 289 all out
South African-born Dutch international Colin Ackermann followed his first-innings 116 with 124 but had insufficient support.
At Lord's in Division Two Marcus Harris followed up his first-innings hundred with a half-century as Lancashire batted out for a draw against Middlesex.
Lancs, set 309 in 67 overs, closed on 8-262 after Max Holden's 184 enabled Middlesex to post 407, the highest score of the match.
Coming in at 2-98 Harris made 52 in 96 minutes before being fifth out, at 174, caught at short third man reverse-sweeping Zafar Gohar.
Back in Division One champions Surrey managed a draw following on at Essex after conceding a 217-run first-innings deficit. England Test wicketkeeper Jamie Smith made 32 and the man he replaced with the gloves, Ben Foakes, 50, while ex-Test bat Dom Sibley top-scored with 66. But England vice-captain Ollie Pope was out for one.
Elsewhere Worcestershire held on for a draw at Taunton, finishing nine down and still 31 runs short after Somerset's mammoth 7-670 dec, and Sussex drew at Warwickshire.
