Warwickshire chased down a Duckworth-Lewis adjusted target of 205 in a match reduced to 42 overs by rain with Pollock unbeaten on 103 off 115 balls out of 207 for 2.
Rob Yates made 60 after Derbyshire were restricted to 200 for 9 by the spin of 17-year-old Jacob Bethell who took 3 for 32 while former Yorkshire bowler Karl Carver claimed 2 for 35.
Pollock said: “The spinners were excellent, Karl (Carver) on his debut for the club, Jacob (Bethell) keeps getting better, we keep forgetting he’s only 17, he’s going to be some player and we’ve not seen his batting yet.
“Lambie (Matt Lamb) only took up leg-spin six months ago and then only started bowling off-spin a week ago. He’s bowled his off-spin to the left-handers and leg-spin to right handers. The three of them were superb, they never really let them off the hook.
“For me, it was very much being there at the end, that’s one of my targets this year. It’s big scores batting first and making sure I finish the job which was my aim here.”
Worcestershire made it two wins from as many Royal London Cup group matches with an 11-run victory over Gloucestershire under DLS in a rain-affected game at Bristol.
The visitors posted 228 for seven from 40.3 overs after losing the toss, opener Jack Haynes leading the way with 59, off 61 balls, with 7 fours and a six.
After three interruptions, Gloucestershire were finally set a target of 94 from 11 overs and could manage only 82 for four, Graeme van Buuren making 38 not out.
Eighteen-year-old left-arm spinner Josh Baker bowled the penultimate over for just four runs, taking the wicket of Jack Taylor to effectively settle the outcome.
Worcestershire coach Alan Richardson said: “We batted positively throughout to reach what I felt would be a competitive total, but once Duckworth-Lewis comes into play you are never quite sure.
“Joe Leach hasn’t played much white ball cricket recently, so it was really good to see him showcase his skills. Historically, he bowls a very good yorker and he has such a calm head on his shoulders.
“I wouldn’t say it was a particularly brave decision to give Josh Baker the penultimate over because it was a tricky pitch to play spin on. But he held his nerve brilliantly.”