It had been three months since the leader last played because of the coronavirus-enforced break, but it needed barely one minute to go ahead through Vidal's header, which hit the back of the net after 65 seconds of play.
Braithwaite then fired in a second eight minutes before the break in a game that also saw the return of Luis Suarez from injury.
Alba struck11 minutes from time before Messi wrapped up victory in stoppage-time as Barca went five points clear of Real Madrid ahead of Los Blancos' return to action on Monday (AEST).
There was no sign of any rust in Quique Setien's ranks.
Frenkie de Jong robbed Real Madrid loanee Takefusa Kubo in midfield and the ball was delivered into the box by Alba, with Vidal running on to the cross and directing his header into the bottom-left corner of the net.
Barca threatened to put the game to bed early on as Braithwaite and Messi both came close before Mallorca finally woke up.
Kubo looked intent on making amends as he forced Marc-Andre ter Stegen into a good save from the edge of the box before being denied again with a low free-kick.
Yet Barcelona doubled its lead before the interval, Braithwaite clinically dispatching his first goal for the club after a scrappy build-up that included headed flick-ons from De Jong and Messi.
Mallorca nearly found a way back into the match shortly after the restart, but Ante Budimir's first-time effort was always bending away from Ter Stegen as it flew wide.
Setien brought on Suarez – out since January because of a knee injury – and that seemed to galvanise Messi, who set up Braithwaite and Ronald Araujo for efforts that were stopped by Manolo Reina and the post respectively.
Messi would not be denied a second assist, however, as he cleverly flicked the ball over the top for Alba, who just managed to stay onside and finish at the near post.
There was time enough for Messi to get on the scoresheet as he kept his balance in the box before working space and firing right-footed high into the net.
Barcelona will host Leganes on Wednesday (AEST) before travelling to Sevilla three days later as the fixtures come thick and fast in LaLiga. Mallorca, which has a crucial clash with Leganes next Saturday (AEST), travels to Villarreal next.