Dropped by Josh Cobb off the bowling of Brandon Glover on 29, Clarke made the most of his extra life as he proceeded to destroy the Northants bowling attack on his way to 136 from 65 balls, before finally being dismissed in the final over.
The 25-year-old hammered an incredible 11 sixes - twice sending the ball out of the ground - as well as six fours as he almost single-handedly powered his side to 214 for seven.
It was the sixth-highest Vitality Blast score of all-time, the 24th best in T20 history, and also the best by a Notts player - beating Dan Christian's 129 on the same ground against the Steelbacks in 2018.
The Northants bowlers were given a torrid time, with the exception of Wayne Parnell, who took two for 30 from four overs, and Tom Taylor (2-36) but Keogh felt it was just a day where everything went right for Clarke.
"It is all about small margins, and on another day we chase down that total," said the Steelbacks batter, who hit 45 from 31 balls as the home side made a great effort to reach 200 for seven in reply.
"We felt a little bit hard done by, as a couple of ours go straight to fielders, while they had a few that landed between three men, but that is how it works some times.
"If Clarkey gets caught early on then the game changes and that is how cricket goes sometimes."
Asked about Clarke's innings, Keogh said: "I regret having a bit of banter with him now about not getting out the powerplay, as he didn't get out until the last over.
"But we know what he can do, he’s done it before and he’s a great player. It can’t be far off until he’s playing international cricket. It was his day."
After losing three wickets in the powerplay, the Steelbacks did recover and with Keogh and Cobb going well there was the chance of the home side pulling off a remarkable recovery as they went from 43 for three to 147 for three in good time.
But Cobb suffered a hamstring injury going for a quick run, which meant Ricardo Vasconcelos had to come on as a runner, and the incident crucially halted the Steelbacks' momentum for a couple of overs, as well as Cobb's timing.
The pair put on 104 before Keogh was caught at deep mid-on going for a third six in three balls, and he said: “It is a tough ground to defend with a fast outfield and a good pitch so the game is never over.
"Cobby and I said we needed to take it as deep as we could without letting the rate get too high and it got to ‘go time’ and I couldn’t the clear the ropes and it was harder for those coming in.
“It is never ideal [to bring out a runner] as it halts momentum but Cobby still struck a few before getting out.
"He played a great hand for us there to put us into a reasonable position to get close."
Cobb was eventually out for 62 from 32 balls, and although Saif Zaib came in and scored 22 not out from 11, the required 27 from the final over bowled by Jake Ball proved too big a mountain to climb.
Pick of the bowlers for Notts was spinner Matthew Carter who claimed one for 15 from four overs, which, along with Clarke's century, proved to be the difference.
Clarke admitted he had to ride his luck during his innings.
“It is all a bit of a luxury in T20 cricket," he said. "I was dropped on 29 and you need that sort of luck in cricket. But to contribute to our first win of the season was good.
“There is never a moment where you look up and think you are getting a big score as every individual ball is different, and you are always looking to take a positive option.
"By doing that you give the bowlers and fielders a chance of being in the game, but it was just my day.”
The Steelbacks have now lost two out of two, both at home, and they are again at Wantage Road on Tuesday night when they host Birmingham Bears.
Head coach David Ripley will be sweating on the fitness of skipper Cobb, but it is hoped the injury is not too serious.