It was a rare moment of class in a scrappy tussle between two sides desperate to get out of the relegation zone.
Without the midfield talent of the injured Wes Hoolahan, Blackpool struggled to find any real rhythm, despite hard-working performances from Claus Jorgensen and Mike Flynn.
The Seasiders created some early chances with Andy Welsh testing Kasper Schmeichel with an early 20-yarder.
The Thompson goal seemed to lift the home side as Cardiff were content to defend their lead and Welsh brought out the best in Schmeichel, who produced a superb save from the winger's cross-shot on 15 minutes.
A minute later it was Schmeichel again who denied another Welsh effort.
Cardiff's moments in front of goal were rare but when Jimmy Floyd Hasselbaink was twice put through he found Blackpool keeper Paul Rachubka in equally good form.
City were content to defend solidly with Blackpool tending to over-elaborate on the edge of the box.
On 50 minutes Schmeichel had to be alert once more to parry away Steve Crainey's goal-bound volley.
On 68 minutes Schmeichel was finally beaten but Gary Taylor-Fletcher's effort crashed to safety off the bar.
Blackpool pushed players forward late in the game and in doing so left holes at the back and Rachubka saved brilliantly from Thompson before Stephen Crainey scooped the ball off his own line from Stephen McPhail.