The Argentinian striker put the Taysiders ahead from the spot in the 21st minute after Killie left-back Garry Hay had clumsily tripped United's tricky midfielder Jennison Myrie-Williams inside the box.
In a game that saw good performances from both goalkeepers, and good chances spurned, mostly by the home side, Casalinuovo was handed his second goal on a plate in the 57th minute when he was set up by Myrie-Williams.
Referee Stevie O'Reilly had a peculiar afternoon in which he made a series of baffling decisions but, although it was enough to enrage the Killie fans in the crowd of 4,753, the official's display had no material impact on a deserved United victory.
Before the visitors got the game going, there was a perfectly-observed minute's silence ahead of Remembrance Sunday.
Killie had a penalty claim in the fifth minute when United stopper Andy Webster eased Kevin Kyle off the ball six yards from goal as the Rugby Park skipper raced to reach a Jamie Hamill cross, but referee O'Reilly, correctly on this occasion, waved play on.
O'Reilly, though, used his whistle all too often in the early stages as a series of free-kicks prevented any flow to the game.
The home side were slightly more forceful and United keeper Nicky Weaver produced a good block from Hamill's angled drive in the 10th minute then foiled Kyle's volley from a similar position after the Tannadice side's offside trap had let them down.
But, in the 21st minute, United took the lead after they were awarded a spot-kick when Hay, back in the side after missing the defeat by Celtic last week, tripped Myrie Williams inside the box.
Noticeably, there were no complaints from Hay and Casalinuovo stroked his penalty past Rugby Park keeper Mark Brown.
Kilmarnock tried to battle back but, to the frustration of the home supporters, they were continually thwarted by the offside flag.
The visitors' defence remained solid in the face of a mostly aerial bombardment and the impressive Myrie-Williams provided a constant threat down the right.
However, in the 37th minute it was United midfielder Morgaro Gomis who drew a fine save from Brown with a 25-yard drive, the Killie keeper diving to his left to turn the ball round the post.
At the other end, moments after Killie had defended the corner, Weaver dealt well with a Gavin Skelton volley that had power but was aimed too close to the keeper, who then made a brilliant point-blank save from Kyle's 12-yard volley two minutes from the interval.
The offside flag continued to punctuate the game after the break, mostly, as in the first half, in favour of the Taysiders.
Some hesitancy in the Killie box in the 52nd minute gave Casalinuovo the chance to double his tally but Brown turned the angled drive from 10 yards past the post and the home side survived the corner.
The second half began to heat up and, at the other end, after good work by Killie midfielder Craig Bryson in burrowing his way into the Tannadice box, James Fowler drove the cut-back over the bar from the edge of the box.
In the 57th minute, though, Casalinuovo sealed the points for the visitors when he grabbed his second.
David Goodwillie's first-time pass sent Myrie-Williams racing into the Kilmarnock box and, when he drew Brown and slipped the ball across the six-yard box, the big striker had the easiest of tasks in knocking the ball into the empty net.
Brown then had to make another fine save from Myrie-Williams as Killie left gaps in pursuit of a lifeline.
Conor Sammon replaced Hamill in the 63rd minute as Jefferies tried another avenue but it was Brown who had to block Goodwillie's drive before Weaver parried Bryson's close-range effort at the other end.
As desperation permeated the home side's play, Kyle did manage to beat the offside trap but volleyed over from 12 yards with only Weaver to beat.
Having done his damage, Casalinuovo was replaced by Danny Cadamarteri in the 75th minute before Mark Burchill came on to make his Kilmarnock debut at the expense of Fernandez.
Killie pressed for the goal that would have ensured an exciting finale but Sammon's wild volley from eight yards, which was more of a clearance than an attempt on goal, summed up a frustrating day for the home side.