The Scot’s well-taken double, within seven second-half minutes, settled a finely-balanced affair which provided little in the way of clear-cut openings in the first half.
That all changed after the break and Miller broke the deadlock with a brave header past onrushing Saints keeper Kelvin Davis from David Marshall’s long ball upfield, before then finishing off good work from Aron Gunnarsson.
It could have been a different story, however, had Saints taken the second-half chances that fell to Rickie Lambert, twice, and Adam Lallana before, in between and after City’s goals.
Substitute Steve De Ridder did grab an injury-time consolation but it is now two games without victory for Nigel Adkins’ side after they salvaged a late draw at Burnley on Saturday, although Saints remain top of the table on goal difference after Middlesbrough could only draw 0-0 at home to Leicester.
Sixth-placed Cardiff, meanwhile, have still only suffered one defeat all season and are now unbeaten in six, although four of those have been drawn.
Saints skipper Dean Hammond dropped to the bench for the first time in a league match this season, replaced by Morgan Schneiderlin, while Cardiff handed starts to Darcy Blake and youngster Joe Mason having lost Lee Naylor, Craig Conway, Robert Earnshaw and Rudy Gestede all to injury.
Southampton, playing their usual brand of well-worked attacking football, started the brighter of the two sides but it was Cardiff who first threatened the scoreline after 15 minutes, Miller seeing his effort blocked by Frazer Richardson.
City weathered the early storm and after Saints striker David Connolly had seen his strike blocked at the other end by Mark Hudson – who shrugged off an ankle injury to start-
went closest to breaking the deadlock just before the half-hour.
Don Cowie combined well with Mason but could only shoot off target from 12 yards when well placed.
Guly Do Prado almost made the hosts pay when he fired narrowly wide for Saints, before Danny Fox and Peter Whittingham sent respective free-kicks over the crossbar.
And as the half-time whistle blew, it remained anyone’s game in the Welsh capital.
The second half proved a much more entertaining affair and Lambert could have headed Southampton into a 50th-minute lead but nodded wide following confusion in Cardiff’s defence.
And the visitors were made to pay for their wastefulness just six minutes later when Marshall launched a long kick downfield and Miller beat Jose Fonte before racing clear to head past Davis and into an empty net.
Marshall proved his worth between the sticks soon after when he produced a terrific save to deny Lallana.
And Miller then made it two-nil when he converted from close range after great play from Gunnarsson.
Lambert was again guilty of heading a clear-cut opening wide of target as Saints were discovering it was not to be their night.
And even though substitute De Ridder pounced to net a 93rd-minute consolation, the Bluebirds held on.