Woakes took 2 for 38 and struck an unbeaten 13 off five balls to take the Bears to 161 for 7 in reply to the Falcons 160 for 8.
Finn Hudson-Prentice top scored for the Falcons with 41 off 22 balls while Dan Mousley hit 56 off 40 for the Bears who won with an over to spare.
Hudson-Prentice said the Falcons had paid the price for not been ruthless enough.
“It was quite a fresh wicket, there was good pace and bounce in the pitch and there wasn't any spin so getting 160 felt like we were 15 or 20 short,” he said.
"We've spoken about being aggressive and taking wickets in the powerplay and I feel we had an opportunity when they were three down for not many but it's a game of fine margins and we fell on the wrong side today."
Luis Reece got the Falcons moving by driving Danny Briggs for six but then top-edged a sweep at the next ball.
Woakes was pulled for six by Harry Came but he shattered his stumps with the next ball as the Falcons were restricted to 47 for 2 at the end of the powerplay.
Billy Godleman cut Jake Lintott to point and Matt Critchley sliced Carlos Brathwaite to the same position before Leus du Plooy drove Lintott to long on.
The Bears had restricted Derbyshire to 26 from five overs but misfields and a missed stumping which reprieved Hudson-Prentice on 21 helped the Falcons post a competitive score.
Hudson-Prentice drove Craig Miles for six and carved him for four in the 18th over but was run out in the next and after Brooke Guest skied Brathwaite to backward square, Michael Cohen ended the innings by lifting Woakes for six.
The Bears started badly, losing Pieter Malan, who bagged a pair in the championship match at Derby, caught at point for a duck off Logan van Beek in the first over.
Ed Pollock was brilliantly caught by Godleman diving at mid off and when Will Rhodes was caught down the leg side off George Scrimshaw, the Bears were 20 for 3 after four overs.
Indisciplined bowling got the Bears back on track with Sam Hain driving Hudson-Prentice for six in an over that cost 14 but then failed to clear long off.
The Falcons regrouped and although Mousley reached his 50 by hooking Scrimshaw for six, Critchley had him caught at long on to leave the Bears needing 35 off the last four.
Critchley took a fine diving catch at long off to remove Michael Burgess for 22 and although Brathwaite holed out to deep midwicket, Woakes hit van Beek for six and four to settle it.