Nigel Clough's return to Pride Park ended in defeat when a late Johnny Russell goal gave Derby a 1-0 win over stubborn Burton.
Burton looked like rewarding former Derby manager Clough with a point and denying their ex-boss Gary Rowett until Russell pounced nine minutes from time.
Derby had given George Thorne his first league start in 18 months and the midfielder had a shot charged down as Burton set out to frustrate Derby.
Matty Palmer forced Scott Carson into a save low to his right following a free-kick and Bywater had to tip over a curling 20-yard effort from Martin in the 19th minute before Tom Lawrence flashed a ball across Burton's six-yard box.
Lawrence glanced a header wide but Burton were working hard all over the pitch to deny Derby space although it needed a great saving tackle by Palmer to prevent Martin getting through in the 34th minute.
Derby were close to taking the lead in the 45th minute when Ben Turner almost turned the ball into his own net as he stretched to clear but Bywater just did enough to keep the ball out.
Burton's game plan had worked in the first half but the extra quality Derby possessed was always going to pose a threat and in the 55th minute, Andreas Weimann made a strong run through the middle but shot straight at Bywater.
Weimann had an even better chance a minute later when Lawrence found him unmarked on the right side of the Burton penalty area but his shot lacked the power to trouble Bywater.
Derby were beginning to put Burton under sustained pressure and Lawrence was the next to test Bywater with a low shot from 20 yards but Burton almost went ahead in the 62nd minute.
Turner rose to meet a corner with a header that was on its way to the top left corner until Weimann leapt to head the ball away but Burton were quickly under pressure again as Derby appealed for a penalty after Lawrence had a shot blocked.
But Burton's resistance was finally broken in the 81st minute when Martin's shot was beaten out by Bywater and a mistake by Palmer allowed Russell to score from 12 yards.
It was tough on Burton but they had a chance to equalise in the final minute of normal time.
A free-kick was only headed out to Lucas Akins but he put his volley wide from 15 yards and Weimann also missed a great opportunity in stoppage-time.