Antonio Floro Flores played the role of match-winner with two goals inside the final five minutes, although Reggina contributed to their own downfall.
The Amaranto, bottom of the Serie A standings and without a win since November 23, did their survival bid no favours as they had two players sent off and missed a penalty before Floro Flores made his mark on the game.
Maurizio Lanzaro was the first player to see red after 55 minutes when he felled Floro Flores in the area, but Reggina looked to have got a slice of the luck they surely need to stay up when Maurizio Domizzi missed the ensuing spot-kick.
If favour was falling their way Reggina did their best to shun it as seven minutes later Antonio Barilla was given his marching orders, for a second yellow card, before Franco Brienza missed a penalty that would have put them ahead with eight minutes to play.
Three minutes later Udinese went ahead through Floro Flores, who had proved a handful most of the afternoon, before he added a second right at the end.
Defeat for Reggina means they remain seven points from safety and, with just seven games remaining, a mountain to climb if they are to remain in the division.
Udinese arrived at Stadio Oreste Granillo looking to bounce back from a 3-1 midweek defeat in the first leg of their UEFA Cup quarter-final tie with Werder Bremen.
They had a glorious chance to take an early lead when with eight minutes gone Alexis Sanchez failed to find the target after Reggina goalkeeper Christian Puggioni had only got fingertips on a cross to leave his goal exposed.
Reggina worked Samir Handanovic at the other end with Fabio Ceravolo's strike from the left forcing the goalkeeper into a good save after 23 minutes.
Handanovic was then well placed four minutes later to block Emil Halfredsson's shot as the game remained deadlocked at the break.
The match livened up in the second half, starting with Lanzaro's dismissal for hauling down Floro Flores in the penalty area. The referee deemed it warranted a straight red card, but Domizzi failed to convert the spot-kick.
Reggina's hopes of getting something from the game suffered a further setback after 62 minutes when Barilla was cautioned for the second time to leave the hosts to play the last 30 minutes with nine men.
Despite their numerical disadvantage, Reggina should have gone ahead with Brienza twice spurning chances.
With 71 minutes on the clock the 30-year-old striker rounded Handanovic only to see his shot cleared off the line by Domizzi and 11 minutes later he saw his penalty palmed away by Handanovic.
It proved a costly miss as Floro Flores finally broke the deadlock three minutes later.
Giovanni Pasquale crossed from the left and while Floro Flores completely missed the ball with his first attempt, he had time for a second effort which he buried low into the bottom left corner.
His second, in stoppage-time, also required two bites of the cherry as he struck his first shot right-footed shot into a defender before the ball fell to his left side which proved more trustworthy as he slid in at the near post.