Leading 1-0 thanks to a Luis Suarez goal from the first leg, Coutinho opened his account for the club and Rakitic later added a second to break Los Che's resolve during the second half, setting up a showdown with Sevilla.
The Blaugrana now have a chance of claiming a record-equalling fourth consecutive Copa del Rey trophy, potentially taking their total tally to 30 titles since the tournament's inception.
The return of striker Simone Zaza appeared to add some much-needed guile to Valencia's attack, and the Italian frontman linked up well with Francis Coquelin, who saw his shot saved down low by Jasper Cillessen.
Los Che continued to look impressive in the opening exchanges and they almost found a route back into the contest when Rodrigo leapt highest inside the area, only to see his looping header cannon back off the crossbar with Cillessen beaten.
Zaza's movement continued to cause issues for both Samuel Umtiti and Gerard Pique, this time as the forward threaded a pass for the run of Rodrigo that was eventually cut out by Sergi Roberto at the vital moment.
Barcelona's most effective moment of the first period came just after the 40-minute mark, when Rakitic turned on the style to pick out the movement of Suarez, although he was hounded out by Ezequiel Garay and Gabriel Paulista as he went to pull the trigger.
Geoffrey Kondogbia missed the first leg but his quality shone in the Valencia midfield, the 24-year-old going close on the stroke of half time as he held off the challenge of Pique before thundering an effort into the side netting.
Coutinho was introduced at the break and it took Barca's new signing just five minutes to break the deadlock, as the former Liverpool man produced an adroit finish on the slide in order to squeeze Suarez's cross back across goal and into the far corner.
The goal all but ended Valencia's hopes of finding a route back into the fixture and Messi almost took full advantage, only to see his rasping drive kept out by Domenech on the hour.
Messi soon returned and should have put himself on the scoresheet after being gifted an opening on the counter, although he was stopped by a standout last-ditch tackle from Gabriel.
Valencia might have stolen a consolation 15 minutes from time when Jose Luis Gaya was left unmarked inside the six-yard box, but he was denied by arguably one of the saves of the season from Cillessen, who flung himself wide on the line to deflect the full-back's effort away from goal.
Rakitic completed Barca's scoring just over five minutes from time, Suarez producing yet more brilliance inside the box to find the Croatian in space and he made no mistake with a drilled finish past Domenech.
VALENCIA (4-4-2): Jaume; Montoya, Paulista, Garay (Vezo '71), Gaya; Coquelin (Guedes '55), Pajero, Kondogbia, Rodrigo (Soler '55); Vietto, Zaza
BARCELONA (4-4-2): Cillessen; S. Roberto, Umtiti, Pique (Mina '83), Alba; Rakitic, Gomes (Coutinho '46), Busquets, Iniesta (Paulinho '65); Suarez, Messi