Michael Chopra worked the ball across field to Thompson, who struck a rasping left-foot drive into the back of the net before Southampton goalkeeper Kelvin Davis could move.
The Bluebirds were unchanged from the side that won at Crystal Palace, while Wales international Gareth Bale recovered from a thigh strain to line up for the Saints.
The visitors applied the early pressure but it was Chopra who went closest to opening the scoring with a well-struck shot that was deflected over the crossbar.
Then Thompson burst through before a firing wide of the target.
The Saints looked dangerous on the break and Darren Purse needed to make a couple of quality tackles to prevent Grzegorz Rasiak and Kenwyne Jones from breaking through on goal.
The visiting goal led a charmed life on the half-hour when Riccardo Scimeca and Chopra both had chances to stab a loose ball home in a crowded goalmouth.
Cardiff did not play with their usual fluency on a night when rain made the pitch slippery but what they lacked in finesse they more than made up for in endeavour, and Thompson was outstanding leading the line.
But the Saints never stopped working and City keeper Neil Alexander was kept busy, making a fine save at the feet of Jones as the striker looked favourite to score.
City made the breakthrough they deserved with just five minutes remaining when Thompson sent the home crowd wild.
Southampton were not finished and they stormed back on the attack in an effort to rescue the point they thought they deserved, but City's defence held firm to secure a fifth successive victory.