There was one change from the Swansea side that beat Cardiff City last time out, with Andrea Orlandi in midfield in place of Joe Allen.
The Rams, who had failed to score in their last three away games, were skippered by former Wales international Robbie Savage.
The Swans had a great chance to open the scoring in the eighth minute when Nathan Dyer raced on to a poor back pass from Gary Teale and after rounding the keeper, his shot went into the side-netting.
Two minutes later a superb move put Darren Pratley into the danger area and there were shouts for a penalty as he went down under a challenge but referee Roger East waved play on.
Craig Beattie had County keeper Stephen Bywater sprawling to save from a Pratley corner in the 27th minute and then Cedric van der Gun fired inches wide as Swansea piled on the pressure.
The half ended with the Swans camped in the Derby end just as they had been for almost the entire first 45 minutes.
Dyer was causing the visiting defence all sorts of trouble in the second half but the final pass just wasn't coming as Derby defended with ten men behind the ball.
When they did breakthrough in the 70th minute, Beattie's shot lacked power and Bywater saved low down.
It took a superb tackle by Savage to deny Dyer four minutes later as the one-way traffic continued.
The breakthrough finally came in the 81st minute when Bassone raced onto a cross-field pass to fire into the net from an acute angle for his first goal for the club. | 
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