Worcestershire 375 for 7 (Roderick 137, Libby 86) beat Gloucestershire 290 (Taylor 121, van Beek 4-58) by 85 runs
Roderick had missed the opening three games in the tournament but continued the excellent form he has been demonstrating in the LV=Insurance County Championship with his List A best score of 137.
He showed his battling qualities in fighting through a testing time with the new ball in seaming conditions after the Rapids had been put in to bat.
But Roderick, who spent eight seasons with Gloucestershire, then accelerated to such an extent that he faced only 114 balls and hit four sixes and 12 fours.
Gloucestershire then lost wickets at regular intervals against the seamers including four for van Beek.
But it only served to bring some respectability to the outcome as Worcestershire sealed a third win in four matches.
Worcestershire made five changes from the side beaten by Somerset at Taunton on Sunday with Brett D’Oliveira, Azhar Ali and Cameron Jones injured and Joe Leach and Dillon Pennington rested.
Netherlands international van Beek was handed his debut and there were recalls for Matthew Waite and Ed Pollock, Roderick and Brown.
Pollock and Roderick were given an examination by Zaman Akhter and Tom Price, who had taken a hat-trick and scored a century on the same day in the corresponding LV=Insurance County Championship match between the sides.
Tom Price made the first breakthrough when Pollock edged to first slip and the powerplay only yielded 24 runs.
Roderick and new batter Rob Jones fought through this challenging period and gradually upped the tempo.
Jones, initially on loan from Lancashire before starting a three-year contract next summer, gloved Anwar Ali through to keeper James Bracey.
But from this juncture bat dominated ball for the remainder of the innings with Roderick in prime form and given superb support by Libby in surpassing the 159 by Tom Fell and Alexei Kervezee at New Road nine years ago.
A single off Paul van Meekeren enabled Roderick to move to three figures and was the cue for a standing ovation.
A straight six by Roderick of Anwar Ali established the third-wicket partnership record against the visitors and it came out of the blue when Libby (86) was pouched low down at gulley off Zaman Akhtar.
Roderick produced the shot of the innings with a reverse scoop for six off Tom Smith but in the same over he sliced the spinner into the hands of short third.
Smith also held onto a return catch from Ben Cox but the innings momentum was sustained by Kashif Ali and new signing van Beek.
Kashif Ali raced to 39 from 22 balls before he pulled Graeme van Buuren to backward square leg but van Beek struck Tom Price for two sixes over long off in making an unbeaten 41 from 19 balls.
When Gloucestershire batted, Matthew Waite bowled an excellent opening spell, beating the bat on several occasions and deserving better figures than 6-1-12-0.
It was van Beek who made the first breakthrough when Bracey holed out to Kashif Ali at wide mid on.
Ollie Price, a century-maker in the recent Championship match at Cheltenham, fell to Ben Gibbon via a sharp catch by Rob Jones at backward point.
Pat Brown came into the attack and three wickets went down inside his first three overs as Gloucestershire subsided to 80 for 5.
Harry Tector was run out after being sent back when he turned Brown to cover and failed to beat Kashif Ali’s throw to Ben Cox.
Van Buuren went lbw and Chris Dent offered a simple caught-and-bowled.
Sub fielder Rehaan Edavalath got into the thick of the action with an excellent diving catch at midwicket to dismiss Tom Price off van Beek.
Libby brought himself into the attack and had Anwar Ali taken at deep cover before Tom Smith was neatly caught down the leg side off Baker.
But Taylor illuminated the dying embers of the game with some big hitting and his century included five sixes and five fours before he and van Meereken were dismissed in successive balls from van Beek.