Coles was promoted up the order and responded by clouting the quickest fifty of the season, from 18 balls, as Essex’s 167 for nine was reeled in with 15 balls to spare.
The Eagles have now lost their past two games – having lost just one of their opening 11 matches - and will be keen to return to winning ways in their final group game against Sussex Sharks on Friday night. That will be their final game before hosting a quarter-final.
Hampshire, who moved into second place in the South Group, are now left relying on Surrey to lose their final two matches to be sure of a home tie in the last eight.
Essex had initially looked like they could defend a slighty disappointing target when Graham Napier trapped Hampshire skipper James Vince lbw with the first ball of the away side’s chase.
But fellow opener Carberry smashed 57 from 28 deliveries to leave his side well positioned.
Even his brilliant effort was eclipsed by Coles, who took full toll of the short boundaries at the Essex County Ground, to blast 54 from 22 balls before he was eventually dismissed by David Masters with just seven required.
Carberry's effort contained seven fours and four sixes, the last of which was huge drive against Masters that carried him to his half-century from 25 balls before Ravi Bopara ended his innings when bowling the left-hander in his first over.
Although Napier returned to trap Glenn Maxwell lbw with a perfect yorker for 25, before the total had moved into three figures, his dismissal only served to herald the arrival of Coles who he unleashed strokes of awesome power that brought him five sixes among eight fours.
Essex also got off to a poor start when Jesse Ryder was bowled for a duck by Will Smith, who went on to undermine the Essex innings as he varied his flight and pace intelligently.
The off-spinner proved so difficult to put away that he picked up his three wickets at a cost of only 17 and among his victims was Ryan ten Doeschate, who struck three sixes in his 36 made from 20 balls before he holed out on the long-on boundary.
Opener Mark Pettini also struck three sixes when making 44 from 35 balls before he was stumped by Adam Wheater as left-arm spinner Liam Dawson tempted him down the pitch.
Tom Westley was the only other notable contributor with the bat for Essex with 31 from 13 balls but the home side failed to provide any momentum, their last five overs producing just 36 runs and the loss of four wickets.
Essex all-rounder Bopara said: "We needed a total of 200 on that pitch and once we fell well short, it was always going to be difficult to contain them.
"We need our top-five batsmen there for 17 overs but that never happened tonight; of course it's disappointing to lose although we know we have a home tie in the quarter-finals.
"We need the momentum of victories and that makes it important we win our final match before going into the quarter-finals a week later."
Hampshire skipper James Vince said: "We went into this game knowing we had to win to stand a chance of a home tie in the quarter-finals and the lads responded magnificently.
“On such a small ground, we took a bit of a gamble playing three spinners but they all rose to the occasion, particularly Will Smith who was magnificent. And then Michael Carberry and Matt Coles saw to it that their efforts were not wasted."