Alaves frustrated Barcelona for the first hour of the match in Catalonia, but Messi opened the scoring with a free kick in the 64th minute, before Philippe Coutinho made it 2-0 seven minutes from time.
Messi then grabbed his second of the clash late on, and Busquets has conceded that Barcelona "found it rather difficult against Alaves" before the Argentine turned on the style.
"We found it rather difficult against Alaves, until a work of art by Messi appeared. We've strengthened well, we have a bigger squad now and hopefully we win the treble," Busquets told reporters.
Barcelona will look to make it back-to-back La Liga wins when they travel to Real Valladolid next weekend.