Worcestershire had to give up home advantage for their quarter-final as New Road was being used by England Lions and Sri Lanka.
It looked like it would not matter when they made 286-9, thanks to a stylish 112 from skipper Jake Libby, this year’s One-Day Cup leading run-scorer, who built on the 54 off 64 balls from Bears old boy Ed Pollock.
Warwickshire looked in deep trouble at 77-5, including the loss of captain Ed Barnard for 29 and then Ethan Brookes’ run-out of his former Bears team-mate Michael Burgess from cover point.
As he dived to stop the Warwickshire keeper’s cover drive, Burgess aborted his run but just too late as Brookes stood up and threw down one stump at the striker’s end.
But Smith eclipsed his previous List A best score of 44 as the game was turned in a sixth-wicket stand of 181 in 163 balls between Smith and Rhodes, who was out with four overs left but they had still done enough to help the Bears get home with six balls to spare.
“It was truly special,” Smith told BBC Radio WM. “In other games I have gone in different situations so it was nice to have a bit of a challenge and see how I could approach that and luckily it went well.
“It was a very long road to start with, but I love batting with Rhodesy and going out there to bat with him. We just looked to enjoy ourselves and take it step by step.
“The nerves were definitely there, but it is just a case of turning them into excitement and I found myself in the zone.”
For all the many connections between the two neighbouring teams, including a Worcestershire side run by Ashley Giles and Alan Richardson, the best was arguably Bears opener Theo Wylie and Pears paceman Jack Home, who were both in the Shrewsbury School first XI this summer and only left last month.