Nalbandian, 28, beat Youznhy 7-6 (7/5), 6-4, 6-3 to record his third win over the Russian in four head-to-head meetings.
The victory for the South Americans ended Russia's 17-match winning streak in the Davis Cup on home turf, which started after the 1995 defeat in the final at the hands of the United States.
"I'm happy with my playing here but I'm not surprised at all though I had no official match practice since April," Nalbandian said.
"I know the level of my average playing and I did my best to prepare for these matches the best possible way."
Argentinian skipper Tito Vazquez said he was happy both with his team's performance and the result.
"Russia were clear favourites ahead of the start with their two top players Davydenko and Youzhny," he said. "But luckily David (Nalbandian) played at his top here winning two points for us.
"Our pair win was also very important. And I think we deservedly won this match."
The first set between Nalbandian and Youzhny went to a tie-break after no break of service game.
Nalbandian, ranked 153rd in the ATP standings, kept his nerve to claim that, with the pair keeping their serves in the second set until the ninth game, when the Argentinian produced a break for a two-set lead.
Nalbandian started the third set with an immediate break for a comfortbale 2-0 lead.
Youzhny, who is currently 14th in the world, battled hard to stay in the game, but Nalbandian managed to maintain his lead to win the set and book his country's semi-final berth against France, 5-0 victors over defending champions Spain.
"Our roster is much shorter than the Argentinian one," Russian skipper Shamil Tarpishchev said.
"I've chosen all our best players for the moment. I'm sure that none of our other players could have strengthened our performance this weekend."
Earlier on Sunday, world number six Nikolay Davydenko battled back from a set down to defeat Eduardo Schwank 4-6, 6-3, 6-1, 6-4 to level the overall scores at 2-2.
"I felt no pressure today as after being beaten in my previous matches here I had nothing else to lose," Davydenko said.
"Though I won I'm disappointed with my playing this weekend. I was playing much better and with much more confidence in my previous Davis Cup matches. I was even thinking of withdrawing from playing today.
"I started poorly today but luckily I managed to find my tennis later in the match and win to level the score."
The 24-year-old Schwank, 52nd in the world, broke early into the match for a comfortable 3-1 lead, which he kept through for a one-set advantage.
In the second set Davydenko broke in the eighth game to pull the scores level at one set all.
In the third Davydenko was in complete command breaking his rival's serve three times to take the set in just 28 minutes.
No big serves were produced in the fourth set before the 10th game, when Davydenko produced another break to win the set and the match.
On Friday, Nalbandian put Argentina into the lead beating Davydenko 6-4, 7-6 (7/5), 7-6 (8/6), while Youzhny put Russia back on track beating Leonardo Mayer 6-3, 6-1, 6-4.
On Saturday Schwank and Horacio Zeballos lifted Argentina 2-1 up beating Davydenko and Igor Kunitsyn 7-6 (9/7), 6-4, 6-7 (3/7), 6-1.