The Eagles came into the clash having not conceded in their last six matches but a powerful drive from Miller and Whittingham's free-kick gave Cardiff the spoils.
Palace may feel aggrieved not to have come away from south Wales without at least a point as they defended stoutly at times but they failed to create any clear-cut opportunities.
Whittingham rattled the bar in the first half, while Miller forced a fine save from Palace goalkeeper Julian Speroni when clean through on goal shortly before he opened the scoring.
Those misses mattered little, though, once Miller and Whittingham found the back of the net as Cardiff extended their unbeaten run to five games to ensure their promotion push gathers momentum.
They were forced to make one change from the side that beat Derby in midweek as Tom Heaton made his first league start of the season by replacing the ill David Marshall in goal.
Mile Jedinak returned to Palace's line-up after being rested for the goalless draw with Portsmouth on Tuesday, while Sean Scannell was recalled, with Jonathan Parr and Darren Ambrose dropping out respectively.
The visitors had not conceded in a remarkable 550 minutes of action but they nearly fell behind after less than three minutes this afternoon when Miller's glancing header from Craig Conway's left-wing cross went narrowly wide.
At the other end, Scannell's fierce 20-yard drive was turned over by Heaton, who held on to Dean Moxey's header from the resulting corner.
The Eagles continued to grow in stature as the half wore on but Cardiff had the best chance when Whittingham's 25-yard strike cannoned off the bar.
The two sides continued to try their luck from distance before the interval but Heaton and Palace shotstopper Speroni were never in danger of having their goal breached.
Conway blazed over from a decent position at the beginning of the second half but defences continued to dominate.
The game looked to be petering out into a stalemate but from out of nowhere, Speroni had to be at his best to deny Miller, who had broke through on goal.
That jolted the home support into action and Whittingham struck wide from just outside the area moments later as Cardiff continued to apply considerable pressure.
And it came as no surprise when Miller fired them into the lead after 67 minutes.
Kevin McNaughton's pass from the right by-line was knocked down by Filip Kiss for Miller, who blasted low past Speroni.
It was the first goal Palace had conceded since John Carew had given West Ham a 2-2 draw at Selhurst Park on October 1.
And it took just another 11 minutes for their defences to be breached once again.
After Jermaine Easter had fouled McNaughton on the edge of the area, Whittingham's free-kick (pictured) found the top corner of the net to settle matters.