The Argentina star missed a penalty in the first half before scoring his first two league goals of the season after the break to seal a second win in two games for Ernesto Valverde's side.
Alaves started their campaign with a 1-0 loss to Leganes last week, but produced a much improved performance against Barca, who had Andres Iniesta back but were without the injured Luis Suarez.
Messi's spot-kick was the best chance of a half in which Barca dominated only to be frustrated in the final third, but the 30-year-old's deflected strike after 55 minutes gave the visitors the breakthrough and took him to 350 top-flight goals.
A second close-range finish followed 11 minutes later and only the crossbar denied him a hat-trick, although 3-0 would have been harsh on the home side.
There was time for Paulinho to make his debut as the Catalans joined Real Sociedad on two wins from two matches and head into the international break on a high.
Valverde opted for a 4-3-3 set-up that included restoring Messi to the false nine role he made his own during Pep Guardiola's time at the club, with Sergi Roberto named at right-back and Aleix Vidal pushed forward into the attacking trident.
Messi and Gerard Deulofeu both forced low saves from Fernando Pacheco in the opening 10 minutes but Barca's dominance of the ball was yielding few clear opportunities.
Indeed, it was Alaves who missed the best chance of the opening half-hour, with Marc-Andre ter Stegen making an excellent near-post save to deny Ruben Sobrino on the break.
Barca were handed a golden chance to break the deadlock before half-time when Rodrigo Ely was penalised for tugging back Gerard Pique in the box, but Pacheco guessed right to keep out Messi's spot-kick low to his right.
But Messi made amends 10 minutes after the break as Barca's number 10 benefited from a stroke of luck. Having done well to get to Jordi Alba's low cross, Messi struck a low left-footed shot that took a big deflection and bounced into the net beyond Pacheco.
It was harsh on the home side, who had defended impressively throughout, but they gifted Barca and Messi a second 11 minutes later to effectively end the match as a contest.
Substitute Paco Alcacer saw a cross cut out but Alexis Ruano's clearance came straight back off the Barca striker's head, allowing Messi to sweep home from 12 yards out.
Messi, who is only the second player to reach 350 goals in Europe's top five leagues after Bayern Munich great Gerd Muller, rattled the crossbar from the edge of the box, but there was to be no hat-trick to celebrate.
