The striker, overlooked for the Spain squad, scored one and had two other goals disallowed as Nuno's side closed to within four points of Real Madrid
Alcacer, overlooked for the latest Roja squad, scored once and had two other goals disallowed as Nuno Espirito Santo's side closed to within four points of Real Madrid and five of leaders Barcelona with an accomplished performance.
It took just two minutes for Valencia to threaten, with Nicolas Otamendi stabbing high and wide from close range after Elche failed to clear a free kick.
Alcacer then pounced on a mistake from Enzo Roco and rounded the goalkeeper but David Lomban was on hand to clear off the line.
Alcacer would later have the ball in the net twice - the first from a corner, and later with a cool low finish - but both times the linesman's flag ruled out the goal.
However, Valencia would ultimately head into the break with an advantage. Pablo Piatti's teasing cross from the left found Sofiane Feghouli at the far post and when Przemyslaw Tyton could only parry his cut-back into the six-yard box, Andre Gomes was on hand to turn home.
Valencia hearts were in mouths shortly after half-time when Diego Alves raced 30 yards from goal to intercept a through-ball, with the Brazilian making enough contact with the ball to escape a foul.
And, just five minutes later, Valencia doubled their lead. Some good work from Feghouli saw him send Gomes clean through to the right of the area and his cross was met by the outstetched leg of Alcacer, who was third-time lucky in his quest to get on the scoresheet.
The impressive Feghouli really should have made it three on the hour mark as he arrived to meet Piatti's cross at the far post but failed to connect properly from point-blank range.
Elche finally created a good chance of their own as Jonathas showed good feet before rifling over from 20 yards, but Valencia soon made the points safe. Feghouli and Gomes combined once again down the right and defender Roco could only contrive to turn the ball into his own net from six yards.
Jonathas again came close from distance, this time forcing Alves into a strong parry, as Valencia took their foot off the gas in the closing stages to cruise to three points.
Los Che sealed an emphatic win in the dying moments as Otamendi rose unmarked from Piatti's corner corner to power home a header with what proved to be the final action of a match that ensured the visitors reduced the gap to the top two ahead of their Clasico meeting.