The former England all-rounder, having already taken 2-24 to restrict the visitors to 251-9, rescued Yorkshire from a perilous position of 50-4 and was still at the crease when Azeem Rafiq hit Luke Fletcher for four to seal victory with two deliveries to spare.
Bresnan struck six fours and two maximums in a brilliant 128-ball knock, sharing 97 for the fifth wicket with Adil Rashid, who was dropped on nought, following a flurry of top-order wickets.
Notts also suffered a collapse, slipping to 46-5 after the hosts won the toss, with David Willey, Bresnan and Liam Plunkett sending Greg Smith, Brendan Taylor and Samit Patel back to the pavilion for ducks.
Openers Michael Lumb and Riki Wessels, who made 36, also departed during the frantic start – to Bresnan and Plunkett respectively – but the Outlaws recovered through an impressive 85-run sixth-wicket partnership in just 16.3 overs from Dan Christian and Steven Mullaney.
After Christian became Steven Patterson’s first victim for 52, courtesy of a brilliant catch from Alex Lees, Mullaney took on the challenge of lifting Notts to a respectable total, helped by the lower order.
Mullaney struck two fours and five sixes in a superb unbeaten 89 off 94 balls while Chris Read, Fletcher and Jake Ball, with 27, produced useful cameos.
Yorkshire made a rollocking start to their chase as in-form Adam Lyth and skipper Lees racked up 45 inside six overs, the former dominating with five fours and two sixes in a 26-ball 39.
But the departure of Lyth to Harry Gurney triggered a collapse that also saw the left-armer dismiss Australian Travis Head before Ball removed Jack Leaning and Lees for the addition of just five runs.
With Yorkshire’s pursuit of 252 in tatters, Rashid and Bresnan were left with an important rebuilding job and the experienced pair responding by taking the score to 147 in the 31st over.
Christian dismissed Rashid for 41 and after fellow England internationals Willey and Plunkett also went, the White Rose still required 47 runs from 55 balls.
Christian struck for a third time with the score on 224, trapping Andrew Hodd leg before, but Bresnan and Rafiq kept cool heads under intense pressure to secure the Vikings’ fourth win in six One-Day Cup outings.
“I was just happy to take it deep and to be there at the end really,” said Bresnan afterwards.
“Me and Rash put on a nice little partnership, and everyone who came in played aggressively and was busy, which helped me at the other end to do my thing, just rotate the strike and hit the odd boundary. I feel in good nick at the moment; and it’s just a case of trying to stay fresh.”
Bresnan deserved a hundred, but all that mattered to him was the end result.
“I did have my eye on it at one point,” he said, “until we got to needing about 30 runs. I thought, ‘I don’t care who gets them here as long as we get over the line’, and Raf came in and played really nicely.”