William Porterfield was the star of the show for the Bears as he scored 83 off just 53 deliveries which included 10 fours and two sixes.
The Dynamos got off to a great start through Phil Mustard and Gordon Muchall who capitalised on the early fielding restrictions to get the home side to 55-0 after six overs.
Both openers were given lives by the Warwickshire fielders as Muchall was dropped on 12 by Chopra and Mustard on 12 by Porterfield.
The two batsmen made the Bears rue these chances by racking up 70 runs inside the first 10 overs especially Muchall who raced to 35 off 25 balls before being caught on the boundary by Andrew Miller off the bowling of Steffan Piolet.
The introduction of Piolet into the Bears attack slowed the Dynamos run rate and his accurate bowling soon got him the wicket of Mustard who was also caught going for one big shot too many as he was caught on the boundary by Jim Troughton.
Ian Blackwell tried to maintain an attacking impetus for the home side as he cracked two big sixes in his innings of 46 but Paul Collingwood couldn’t match that total, hitting seven off 10 balls and was eventually was caught by Porterfield off the bowling of Darren Maddy.
Dynamos new-boy David Miller came in with four overs to go and tried to up the Durham run rate with Blackwell but pinpoint bowling from Neil Carter and Keith Barker restricted the home-side to 151 runs off their 20 overs.
The Bears came very quickly out of the traps at the Durham opening bowlers Graham Onions and Chris Rushworth with Carter blasting the seamers twice over the rope in his cameo innings of 18 from 8 deliveries.
When he was removed by Rushworth, Porterfield came to the crease and dominated the Dynamos quick bowlers from ball one.
The Irishman shared partnerships of 41 with Varun Chopra (11) and 44 with Troughton (18) to put the Bears into a winning position.
Gareth Breese did his utmost the keep the home-side in the game with his accurate spin bowling as he grabbed the wickets of Chopra and the Warwickshire skipper to give the Dynamos a chance of victory as he finished with figures of 2-24 off his four overs.
Durham captain Dale Benkenstein did all he could to stop the runs from Porterfield but the Irishman kept finding the rope and looked to be taking his side over the victory line before he was run out by the skipper just one run short of the winning total.
His departure did not stop the Bears reaching the target of 152 as Rikki Clarke hit the winning runs off Mitchell Claydon to give the visitors the victory in the 19th over.
The Dynamos next t20 games is against Worcestershire on Sunday at New Road, where they will hope to get back on track and register their first win of their 2011 t20 campaign.