It was Miller again who threatened moments later, as he rose to meet a cross from David Perkins, but put his header over the bar.
Blackpool saw another chance go to waste a few minutes later when Perkins directed a strike wide from the edge of the box.
Whittingham came close for the visitors just before the break, but he could only fire his free kick over the bar.
As the game entered the 53rd minute a small number of Blackpool fans left the stadium as part of a protest against chairman Karl Oyston.
In the 64th minute Blackpool took the lead through Francois Zoke, who drove into the box before firing a low strike into the bottom corner past Marshall.
Delfouneso almost scored a second for hosts, but saw his strike saved by Marshall, before Adam Le Fondre fired over the bar from close range for the Bluebirds.
Cardiff dominated the possession in their search for an equaliser, but they could not find a way through the Blackpool defence as Jose Riga's team ended their 10-match winless run in the league.