Doubles for Luis Suarez and Paulinho secured the victory for Ernesto Valverde's side at Camp Nou, where Deportivo, who are battling to avoid relegation, offered little to trouble the Catalan giants.
While the hosts won with ease, the absence of the Video Assistant Referee (VAR) system from Spain's top flight, where it will be introduced next season, again appeared to cost Barca what would have been a stunning rabona goal from Suarez in first-half injury time.
The Blaugrana also lost Alcacer to a muscle injury in the first half, leaving the forward out for three weeks and rendering him unavailable for the all-important showdown with struggling title holders Real Madrid at the Santiago Bernabeu next Saturday.
Andres Iniesta was withdrawn as a precaution with the match won early in the second half, while key men Suarez and Lionel Messi, who was impressive throughout and orchestrated his team's attack but missed a second-half penalty, appeared to emerge unscathed.
The match was played at a low-key tempo for much of the first half, but Barcelona were firmly in charge throughout and saw a Suarez goal ruled out for offside as early as the sixth minute.
Messi twice drew saves from Ruben Martinez, as did Aleix Vidal, who came on as a substitute to replace Alcacer with 21 minutes gone.
The deadlock was broken in the 29th minute, when Ivan Rakitic's corner was only cleared as far as Iniesta, who lifted the ball back into the area and picked out Messi perfectly. The Argentine in turn squared for Suarez to stroke home from close range.
The former Liverpool star turned provider for Messi to hit the crossbar in the 37th minute and it was 2-0 four minutes later, the woodwork this time unable to save Deportivo. A Messi shot struck the inside of the upright and bounced clear, but Paulinho was on hand to poke home the rebound.
Suarez thought he had netted a third in injury time, the Uruguayan conjuring up a brilliant rabona finish at a tight angle, only for Ruben to claw the ball away. The presence of VAR might have seen a goal awarded in Barca's favour, but the hosts had to be content with a 2-0 lead going into the half-time break.
They did not have to wait long for that third goal to arrive, though, Sergi Roberto swinging a pass into the back post for Suarez to smash past Ruben and complete a slick counter-attack just a minute into the second half.
Iniesta, increasingly fragile in the twilight of his career, was replaced by Andre Gomes in the 56th minute.
Messi only had himself to blame for spurning a chance to score from 12 yards out in the 70th minute, the Argentine hitting the frame of the goal yet again after Suarez was fouled by Federico Valverde.
Instead it was Paulinho in the right place at the right time with 15 minutes to go, the Brazilian bundling the ball home after Jordi Alba's shot struck the post and left Ruben stranded.
