Lionel Messi and Neymar hit second-half braces for Barca after Gerard Pique celebrated his 200th La Liga appearance with a volley that clipped off Domingo Cisma and into the roof of the net 10 minutes before the break.
Neymar was upended in the box by Sergio Pelegrin and Messi scored the penalty after 55 minutes. Elche midfielder Faycal Fajr was dismissed for a second yellow card two minutes later.
Messi was the provider twice for Neymar who finished clinically after 69 and 72 minutes before the Argentine got his second two minutes from the end.
Messi has now equalled the record of doubles scored in La Liga after notching up his 77th to match the total set by Telmo Zarra, of Athletic Bilbao, in the 1940s and 1950s. It is the latest in a long line of records for the striker, who became the highest scorer in La Liga history earlier this season.
There was still time for Pedro to get the sixth from close range after being found by Neymar.