Neither side was able to produce enough chances to warrant a first-half lead, while Palace goalkeeper Julian Speroni was perhaps fortunate to only collect a yellow for handling outside the area.
The hosts then went on the claim victory with Ambrose striking from the edge of the area before Johannes Ertl was denied by the bar.
Palace were without Freddie Sears and Claude Davis with the on-loan West Ham striker Sears struggling with an ankle injury while the ex-Rams defender Davis was still hampered with a hamstring problem.
Rams boss Nigel Clough threw James Vaughan straight into his starting line-up after securing the striker on a three-month loan from Everton on Friday.
In a quiet start to the game Johannes Ertl, in his first start of the season, produced an early strike, firing wide of Derby's goal from outside the area.
Vaughan had the first real chance in the 10th minute but the 21-year-old failed to keep his strike from 12 yards down.
Speroni found himself in trouble in the 20th minute when he was booked after handling outside the box, but the Argentinian was able to deal with the free-kick.
The goalkeeper was in action again five minutes later as he did well to deny Tottenham loanee Jake Livermore from close range.
The hosts resorted to a string of long-range efforts just after the half-hour mark with Neil Danns firing wide before Derby keeper Stephen Bywater collected efforts from Ertl and Danns.
Bywater then produced a spectacular save to deny Ambrose, who did well to hit the target with an overhead kick.
Derby Gary Teale produced the first strike of the second half, firing wide from 18 yards.
But it was Palace who broke the deadlock 10 minutes after the break when Sean Scannell headed the ball on for Ambrose to find the bottom-right corner from the edge of the area.
The former England Under-21 midfielder's strike was Palace's first goal at Selhurst Park in four.
A quiet spell proceeded the goal but Palace came agonisingly close to doubling their lead in the 69th minute when Ertl headed against the bar after latching onto an Ambrose free-kick.
Striker Rob Hulse had the chance to pull Derby level shortly after but he failed to hit the target from 12 yards before Bywater did well to deny Ambrose and Palace their second.
Derby's troubles were added to when Miles Addison was forced off due to injury with 10 minutes remaining, prompting the introduction of Kris Commons.
Both sides had late chances with Ertl striking wide while Danns was denied by Bywater before Speroni denied Commons.