The powerful South African blasted an unbeaten 110 off 62 balls, with 15 fours and four sixes, as his side ran up 206 for three after losing the toss. Alex Wakely contributed 35 and Steven Crook a rapid 27 not out.
In reply, Gloucestershire plunged to 21 for three as David Willey (four for 32) claimed three for five from his first two overs.
Alex Gidman, who blasted 49 off 19 balls, and Ian Cockbain (60) ensured respectability, but they were never seriously in the hunt and closed on 189 for six.
The result means Northamptonshire join Glamorgan on eight points from five games at the top of the Midlands/Wales/West Division, while Gloucestershire can forget the quarter-finals, having lost four of their first five matches.
After taking a few deliveries to gauge the pitch, Levi cut loose with a series of meaty cuts to go with his trademark leg-side shots.
He lost opening partner Kyle Coetzer to the first ball of the fifth over, caught by Gidman at mid-wicket off Tom Smith for 15 with the total on 31.
It was 49 for one at the end of the six overs of power play and with two runs added Cameron White, on 10, was caught on the deep mid-wicket boundary by Dan Christian pulling a delivery from Benny Howell.
Wakely then helped Levi add 89 for the third wicket in 8.4 overs, hitting two straight sixes in an over off the left-arm spin of Chris Dent in his 24-ball innings, which helped take the score to 140 for three.
The Northamptonshire skipper was annoyed with himself for giving a catch to long-off in the 16th overs, giving Howell as second wicket.
But there was no dislodging Levi, who moved to his century with his fourth six, hammered over mid-wicket off Dent in the 19th over.
Crook joined the party with two sixes of his own, one of them bringing up the 200 in the final over, bowled by David Payne.
Left-arm spinner Smith escaped the carnage with creditable figures of one for 25 from his four overs.
Gloucestershire were left with a mountain to climb after Willey sent back Hamish Marshall, Michael Klinger and Dent to leave them 21 for three in the fourth over.
After 10 overs the hosts had made only 65 for four. But Gidman at least made a fight of it with four sixes and as many fours as the only home player to match Levi's power.
Cockbain played well without reaching the necessary tempo and got to fifty off 43 balls in the 19th over, but by then the cause was lost.
- Sports & Recreation
- David Willey
- Alex Gidman
- Alex Wakely
- Steven Crook