Madrid have two games in hand, the first of which was supposed to take place on Sunday at Celta Vigo.
However, that match has been called off after strong winds damaged Celta's Balaidos stadium and left it unsafe to hold the game, La Liga confirmed after a security evaluation was carried out by local authorities.
Barca took their chance to apply pressure at the Camp Nou, but needed some wasteful finishing by Athletic in a much tighter game than the scoreline suggests.
"Today a lot of players who haven't had a lot of minutes took part and showed what they can do," said Barca boss Luis Enrique yesterday.
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"We were able to give a rest to some because, without that, it is impossible to compete at 100 percent with all the games we have coming up.
"Thirdly, we've won three marvellous points."
Alcacer has endured a torrid time since joining Barca but settled the hosts when he turned home Neymar's cut-back inside Gorka Iraizoz's near post.
Athletic's day was summed up with Barca's second, five minutes before half-time. After scoring in both legs of the Copa del Rey last 16 clash between the sides from free-kicks last month, Messi again outdid Iraizoz from the narrowest of angles.
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This time, though, the goalkeeper was more at fault than brilliance from the Argentine as Messi registered his 31st goal in 30 games this season.
Only injuries to Gerard Pique and Rafinha blighted Barca's day. Pique limped off at half-time as a precautionary measure with a groin strain, whilst the Brazilian suffered a knock in clashing with Ter Stegen.
Messi then took a rare break as he was replaced by Sergi Roberto.
Yet, even that change worked in Barca's favour as Aleix Vidal was pushed into a more advanced role from right-back and rounded off the win by firing into the far corner 23 minutes from time for the Catalans' 100th goal in all competitions this season.
the postponement, saying the stadium "will not be secure for players and fans".
Celta's Galician rivals Deportivo la Coruna saw their clash with Real Betis on Friday also postponed due to weather-induced damage to Deportivo's Riazor ground.
Elsewhere, Atletico Madrid strengthened their hold on the final Champions League position in fourth as Fernando Torres scored twice to see off lowly Leganes 2-0 at the Vicente Calderon.
Torres won the penalty that led to the opening goal on 15 minutes as he was chopped down by Dimitrios Siovas.
For the fifth time in his seven penalties for Atletico, Antoine Griezmann failed to find the net as Iago Herrerin saved his tame effort, but Torres poked home the rebound for his first league goal since September.
At the other end of the table, Valencia's struggles continued as they were thrashed 4-0 at home by Eibar to remain six points above the relegation zone in 15th.