Ramos opted to omit winger David Bentley from the matchday squad altogether, with Luka Modric having to settle for a place on the bench.
The home side made the early running, with Andrea Coda heading Gaetano D'Agostino's free-kick from the left narrowly wide of the far post in just the fourth minute.
Fifteen minutes in Spurs hit back as Jermaine Jenas made a fine break down the right, but his cross into the area was headed weakly straight at keeper Samir Handanovic by Darren Bent.
Aaron Lennon then forced a block from Handanovic at his near post, as the visitors started to find some rhythm in their play.
However, they were rocked midway through the first half as keeper Heurelho Gomes miscontrolled a backpass and then slipped over, before hauling down Fabio Quagliarella to concede a penalty.
Antonio Di Natale made no mistake from the spot, burying his effort into the corner of the net past the despairing Gomes.
The remainder of the first 45 minutes was a tepid affair, with neither keeper seriously extended, although both looked shaky from set-piece deliveries.
At half-time Modric took over from Benoit Assou-Ekotto, with Gareth Bale moving to fill in at left-back.
Five minutes into the second half Gomes was forced into a fine low save after Quagliarella found space on the edge of the area to get in a right-foot shot.
Then Spurs' plight got even worse as Jamie O'Hara was shown two yellow cards in the space of a minute and was sent off by German referee Felix Brych.
Soon after the hour mark Di Natale looked set to double the lead, but Gomes somehow recovered his ground to claw the striker's lob away as it was dropping towards the far corner of the net.
Spurs rarely looked like finding an equaliser before, six minutes from time, substitute Giovani lofted in a fine cross from the right and Bent's firm header forced a spectacular save form Handanovic.
However, Udine sprang forward on a quick counter-attack and the ball eventually landed at the feet of Simone Pepe, who took his time to coolly beat Gomes from 12 yards to make the final score 2-0.