Clarke produced a stunning innings of 136 from just 65 balls to power the reigning champions to 214 for seven in their 20 overs, and that proved to be too many for the Steelbacks despite a valiant effort in reply as they hit back with 200 for seven.
Josh Cobb hit an excellent 62 from 32 balls and Rob Keogh 45 from 31 as the County at one stage looked capable of pulling off what would have an extraordinary win, but the target proved to many.
Outlaws opener Clarke hammered 11 sixes and six fours, twice hitting the ball out of the ground, but it was also an innings that should never have been, as he was dropped by Cobb when on just 29.
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Clarke certainly punished the Steelbacks, who have got their campaign off to the worst possible start, having also lost their opener at home to Worcesteshire Rapids on Friday.
Outlaws won the toss and got off to a decent start under blue skies at the County Ground, with Clarke hitting one towering straight six off Ben Sanderson, the ball bouncing on the roof of the Lynn Wilson Centre.
They had eased to 31 for none when Brandon Glover struck in the fourth over.
Alex Hales had smacked the first two balls of the over for six and four over point, but when he tried to hit the Netherlands international down the ground off the third he sliced his shot and Cobb ran back to take the catch at mid-off.
Glover had made the breakthrough, but the over still went for 16.
By the end of the powerplay, Notts were well set at 53 for one, with Clarke unbeaten on 27 from 18 balls.
He should have been out in the seventh over, miss-hitting a Glover delivery to Cobb at mid-off, but the skipper spilled the chance diving forwards.
To rub salt in the wounds, Clarke then hammered the last ball of Glover's over for six over mid-wicket.
That drop looked like proving very costly as Clarke sent another ball out of the groun in the ninth over, despatching a Tom Taylor full toss over the old scoreboard and into the gardens beyond.
He brought up his 50 from just 28 balls, and with Notts 98 for one at the halfway stage, things were not looking good for the Steelbacks.
They got a much-needed second wicket in the 12th over, with Peter Trego hammering a Graeme White delivery to Ricardo Vasconcelos on the mid-wicket boundary, and he held on.
Clarke carried on plundering the runs, hitting two sixes off White in the 14th over, but there was some joy for the left-arm spinner as he claimed the wicket of Tom Moores, caught by Sanderson on the boundary.
There was not stopping Clarke though and he brought up his century with his eighth six, this time hammering Taylor back over his head to reach his ton in just 49 balls.
Wayne Parnell bowled Steven Mullaney with a yorker to leave Notts 184 for four, but the misery continued for the Steelbacks in the 18th over.
Glover was forced out of the attack for two waist-high no balls for height, the second of which actually saw Clarke caught by Rob Keogh on the boundary.
Parnell pulled off a stunning caught and bowled to dismiss Samit Patel, before the Steelbacks finally got rid of a tired Clarke in the final over as he hit Taylor down Saif Zaib's throat at deep mid-off for a quite brilliant 136 from 65 balls.
The Outlaws closed their innings on 214 for seven, and that was going to be a tall order to chase down.
The reply got off to a bad start as Richard Levi sent a skier to Hales off the spin of Matthew Carter and the home side were seven for one.
Adam Rossington clubbed a couple of sixes, and there was also one for Vasconcelos, but both were out before the end of the powerplay, caught going for big hits, as the Steelbacks were reduced to 43 for three.
Cobb signalled his intent as a four and two sixes from his first five balls saw the opening six overs end with the Steelbacks 57 for three.
The skipper and Keogh batted well and kept the scoreboard moving, and by the halfway stage the Steelbacks were 90 for three, still needing 125 to win.
Cobb brought up his 50 off just 22 balls in the 13th over, having hit three sixes and five fours, as Steelbacks powered to 128 for three.
Vasconcelos had to come on as a runner as Cobb suffered what looked like a hamstring injury going for a quick run, and it meant the innings lost some momentum
Keogh weighed in with some big hits though and had moved to 45 from 30 balls when he perished, caught on the long-on boundary going for what would have been a third six in a row.
That left the Steelbacks on 147 for four with five overs remaining.
Cobb, clearly troubled by his injury, was out for 62 from 32 balls as he was caught on the mid-wicket boundary.
The equation was 58 to win from the final three overs with Parnell and Zaib at the crease, and the Steelbacks were still in the hunt as the first two balls of the 18th went for four.
But Parnell went for 14, and the rate required proved just too much as 43 was required from the last two overs, despite another great effort from the Zaib.
The Steelbacks needed 27 off the final over, but former England man Ball was too good as the home side close on 200 for seven, with Zaib hitting the last ball of the match for six to end 22 not out from 11 balls.