Azhar Mahmood was the star performer for the New Zealand side as the former Pakistan all-rounder took five for 24 from his four overs, then belted 55 not out to see his team home.
The 37-year-old from Rawalpindi plundered four sixes and five fours in his belligerent innings, after removing James Vince, Jimmy Adams, Shahid Afridi and Liam Dawson with the ball.
Hampshire posted 121 for eight from their 20 overs, but it proved hopelessly insufficient as Auckland reached their victory target with 5.3 overs remaining, for the loss of just two wickets.
It was a hugely disappointing defeat for Giles White's team, who won both the Twenty20 Cup and the CB40 in the English domestic season.
Michael Carberry provided the lone resistance for the English side with a run-a-ball 65 before he was caught one-handed by Lou Vincent on the boundary in the final over
Afridi, who failed in a four-ball duck with the bat, took a solitary wicket, as did first-change bowler Chris Wood, but it was a stroll for the Auckland batsmen who dealt better with a slow, sticky wicket at the SuperSport Park.
The defeat sees Dimitri Mascarenhas’s side fall at the first hurdle in the 20-over competition in South Africa, with $6 million prize money on the line.
Hampshire's second match, against Pakistan side Sialkot Stallions on Thursday, will be all but a dead rubber.
Yorkshire reached the group stage of the Champions League Twenty20 with a six-wicket win over Trinidad & Tobago.
A stand of 93 between Darren Bravo and Denesh Ramdin took T&T to 148 for nine despite Ryan Sidebottom's excellent figures of three for 13.
Yorkshire's reply started slowly but Gary Ballance (64 not out) and Adil Rashid (33no) saw them home with an unbroken stand of 103.
The Caribbean side won the toss and batted but slipped to eight for three as Joe Root had William Perkins superbly caught on the straight boundary by Ballance and Lendl Simmons and Adrian Barath fell swinging recklessly.
Steven Patterson's second over went for nine including a six for Bravo and Azeem Rafiq also gave up nine from his first over as Bravo and Ramdin fought back.
Ramdin brought up a half-century partnership in the 11th over with back-to-back boundaries off Rafiq and lifted the spinner for six to move into the thirties from 20 balls before Bravo fell five short of a half-century, skying Rashid to Ballance at long-on having hit three fours and two sixes.
Ramdin reached a 35-ball half-century with an improvised boundary as Patterson prevented a pre-emptive ramp shot. It was his sixth four to go with that one maximum, but he was then run out by Root for 59 from 40 balls. Kevon Cooper (15) and Ravi Rampaul (six) put on 18 before falling to successive Sidebottom deliveries.
Yorkshire lost Phil Jaques for six and Andrew Gale for two, leaving Root and Adam Lyth to rebuild from 16 for two. They put on 28 before Lyth (18) was bowled by Rayad Emrit, who had shockingly dropped him two overs earlier, and Root (16) chipped a simple return catch to Yannick Ottley to leave the Tykes 51 for four in the ninth over.
Rashid raced to 22 from his first 11 balls, with three fours and a six, and a six from Ballance - his first boundary - took the partnership beyond 50.
The left-hander hit three more maximums before a lofted edge slipped through Rampaul's hands for his first four, leaving 17 needed from the last three overs. When Ballance reached a 32-ball half-century with a boundary off Rampaul, Yorkshire could scent victory, and he launched two more sixes to wrap up their qualification with seven balls to spare.
- Gary Ballance
- Denesh Ramdin