Valencia leapfrogged Atletico into third last weekend with their fifth victory in six games and their latest success means the champions need to beat Getafe at the Calderon on Saturday to trim the gap back to a point with 10 games left.
Valencia have 60 points from 28 matches, four adrift of second-placed Real Madrid, who are a point behind leaders Barcelona ahead of Sunday's 'Clasico' at the Nou Camp.
Gomes fired Valencia ahead a minute before halftime at Elche's Martinez Valero stadium and Alcacer made it 2-0 when he stabbed in a Gomes cross in the 57th.
Enzo Roco contributed to a depressing night for 15th-placed Elche, who are hovering just above the relegation zone, when he turned the ball into his own net 19 minutes from time.
Valencia centre back Nicolas Otamendi then headed powerfully home at a corner in the second minute of added time.
"We are in very good shape," Gomes said in an interview with Spanish television.
"We scored four tonight and we could have scored more and I think the fans are very happy," he added.
"Our goal is to play in the Champions League next season and we are in a good position in the table to make that happen."
Buoyed by their recent takeover by Singapore billionaire Peter Lim, Valencia are making a strong push to claim Spain's third automatic Champions League berth after missing out on a place in Europe last term.
Finalists in Europe's elite club competition in 2000 and 2001 and La Liga title winners in 2004, they are hoping Lim's investment will help them regain their status as genuine challengers for silverware in Spain and Europe.
(Writing by Iain Rogers, editing by Ken Ferris)
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