Durham never looked like overhauling Hampshire's formidable 8-221 at the Riverside on Friday, falling well short despite Ollie Robinson's unbeaten 60 from 33 deliveries.
Hampshire, who have won this competition three times, with their last triumph coming in 2022, appeared on course for a massive 250 after an early onslaught from Toby Albert and Australian Chris Lynn.
The pair smashed 90 from six overs and took the score to 112 when Lynn (51 from 27 balls) fell to legspinner Nathan Sowter.
Albert departed in the next over having made 68 from 37 balls (seven fours, four sixes), but James Vince and Australia's Cartwright ensured there would be no mid-innings wobble.
Skipper Vince struck 27 from 19 balls and Cartwright, despite the late fall of wickets, cracked 61 from 31 for the Hawks to post a challenging target.
Durham reached 50 in the sixth over, but batters failing to build on promising starts hurt them.
David Bedingham offered a legside catch off Scott Currie for 22, and skipper Alex Lees went for 26 after also picking out a fielder.
Colin Ackermann was run out by a brilliant Chris Wood throw from behind the wicket.
Durham's race was run after the departure of Ben Raine left them 5-110 in the 11th over, with Robinson dragging them towards respectability.
Benny Howell finished with 2-28 as Durham ended on 6-195 and Hampshire booked a record 11th finals day.
