Morgan replaced Brendon McCullum as skipper, with scheduled stand-in Dawid Malan away on international duty, but saw his side slip to a six-wicket defeat.
Having won the toss Morgan elected to bat, and despite him adding 22 runs to opener Stevie Eskinazi's 43, the hosts were bowled out for 136 with five balls unused.
And Hampshire raced to a fifth victory of the campaign, with Rilee Rossouw hitting 60 from 47 deliveries as the visitors won with 15 balls to spare.
Elsewhere in South Group on Thursday, leaders Glamorgan lost a rain-affected game against Gloucestershire by five runs.
Thisara Perera bowled Jacques Rudolph with the last delivery before the rain delay, which proved crucial in securing victory.
Phil Mustard's 57 helped Gloucestershire to 150 for nine batting first and Glamorgan were 32 for two after five overs when play stopped.
Sussex wasted little time handing Surrey an eight-wicket thrashing.
Surrey recovered to 148 for eight having been 86 for five, with Tom Curran (20) and Ollie Pope (34) enjoying a 56-run stand for the sixth wicket.
But Sussex chased that down in just 13-and-a-half overs, with Chris Nash and Stiaan van Zyl combining for 120 runs before Surrey took a first scalp.
Derbyshire are top of North Group after beating Yorkshire by five wickets at Headingley.
Billy Godleman's second half-century of this season's competition helped the visitors chase Yorkshire's 180 for five with two balls to spare.
Pakistan captain Sarfaraz Ahmed scored 42 for Yorkshire, but Godleman and Wayne Madesn (47) laid the platform for the chase, with Alex Hughes and Gary Wilson (33 not out) hitting 13 runs off Tim Bresnan's final over to secure victory.
A stunning 77 from Ryan McLaren could not lead Lancashire to an unlikely win against Northamptonshire, who prevailed by 11 runs.
It looked like game over when Lancashire were 25 for five chasing Northants' 158 for four - boosted by opener Richard Levi's 71.
Rory Kleinveldt took two wickets in his first over, while Richard Gleeson got rid of England duo Liam Livingstone and Jos Buttler.
But McLaren and Dane Vilas (40) then put on 91 in the next 10 overs, and McLaren took the game into a final over.
Needing an unlikely 26 off the last six balls, McLaren hit successive sixes but then holed out to mid-off from the third delivery, and Kleinveldt conceded just two more runs to secure victory.
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