Lionel Messi scored his 17th and 18th goals of the season to move clear as the division's top scorer, helping Barcelona return to winning ways in La Liga.
Ronald Koeman made wholesale changes to the side that was held to a 1-1 draw with Cadiz, with Trincao one of five fresh faces. The Portuguese was Barca's most dangerous outlet in the first-half, twice opening up the visitors' defence but repelled by goalkeeper Edgar Badia on both occasions.
Elche - embroiled in a relegation battle - went in level at the break, but had their chances in the opening 45 minutes. The unmarked Lucas Boye went closest when he inexplicably blazed over from point-blank range.
But Messi took matters into his own hands to give Barcelona the lead, slaloming through a crowd, exchanging passes with Martin Braithwaite before firing past the goalkeeper.
That goal put him one ahead of former teammate Luis Suarez in the race for the golden boot, and Messi soon added a second to put the game beyond the visitors, latching onto Frenkie de Jong's cutback before coolly lifting it over Badia.
Barcelona's commanding second-half display was capped with a third goal, and Messi was involved once again. His absorbing pass found Braithwaite, whose cushioned header set up Jordi Alba's for his second goal of the season, as the Catalans put their recent woes behind them for a morale-boosting win.
The result lifts Barcelona above Sevilla into third, just two points behind Real Madrid and five behind leaders Atletico.