Two goals in three first-half minutes, from Stephane Mbia and Carlos Bacca, settled matters at the Ramon Sanchez Pizjuan, and gave Unai Emery the upper hand against his former team.
Sevilla, UEFA Cup winners in 2006 and 2007, headed into the game as favourites on league form, having won seven of their last eight matches, but had yet to beat Los Che this term.
Both sides made a lively enough start to the all-Spanish affair, as they battled for the right to meet Benfica or Juventus in Turin next month.
Beto was the first goalkeeper to be called into action, the Sevilla stopper brilliantly parrying a 25-yard Juan Bernat blast in the 17th minute, but it was the hosts who looked the more dangerous going forward in the early stages.
Federico Fazio and Daniel Carrico headed narrowly wide from Ivan Rakitic corners, before the opener arrived on 33 minutes. Rakitic's free-kick from the left was met by Mbia, who lashed into the top-right corner from close range.
And the home fans had hardly finished celebrating when Bacca doubled their advantage, latching onto Machin Vitolo's pass and despatching a low shot past Vicente Guaita.
The Valencia goalkeeper pulled off a fantastic save shortly before half-time to keep his side only two goals down at the interval, beating away a Fazio header from another Rakitic set-piece.
Guaita needed to remain alert after the interval as Sevilla continued to press for a third goal, with Rakitic pulling the strings. The Croatia midfielder first found the head of an unmarked Fazio with a free-kick and then fed a through-ball into the path of Bacca, but both chances were snuffed out by the visiting keeper.
Juan Antonio Pizzi's side should have halved the deficit in the 66th minute when Carrico's poor clearance fell for Eduardo Vargas just inside the box, but his curling attempt drifted inches wide with Beto beaten.
The visitors were looking determined to get at least an away goal to show for their evening's work and finished the match on the front foot, but were unable to find a way past Beto.
Substitute Jonas' close-range effort was parried by the Portuguese and then the impressive Vargas headed against the bar.
Vicente Iborra was introduced from the Sevilla bench just before the end and could have added to Valencia's woes by scoring with his first touch after shaking off his marker in stoppage time, but drilled his shot into the ground and over the bar.