The team often described as the best in the world had drawn with Sporting Gijon and lost to Arsenal in the Champions League and when Bilbao's Andoni Iraola levelled with a second-half penalty at the Nou Camp, they were clearly rattled.
With Real Madrid having narrowed their lead at the top to two points with a comfortable 2-0 win over Levante on Saturday, Barca were uncharacteristically rushed as they poured forward looking for the winner.
"We couldn't allow ourselves another slip up because Madrid were close. Every game is vital," Messi told Spanish television.
"Bilbao were very organised in the way they put us under pressure and played very well. These are three important points."
Barca moved on to 65 points from 24 matches with Real on 60.
Fourth-placed Villarreal's faltering form continued when they were held 1-1 at home by basement side Malaga and Osasuna's new coach Jose Luis Mendilibar led his team to a stunning 4-0 win over sixth-placed Espanyol.
The goal of the day came from Deportivo La Coruna goalkeeper Daniel Aranzubia, who headed a last-ditch equaliser for a 1-1 draw at Almeria.
Barca's 16-match winning streak in the league ended with a 1-1 draw at Sporting last weekend and a 2-1 defeat at Arsenal in the Champions League on Wednesday suggested the Spanish champions were suffering a dip in form.
CUSHIONED VOLLEY
Those doubts appeared misplaced when Xavi's diagonal pass over the defence found the overlapping Dani Alves who cushioned a volley inside for Villa to fire first time into the corner after only four minutes.
For all their domination, however, they could not find a second and when Sergio Busquets brought down Fernando Llorente for a penalty, Iraola's 49th-minute spot kick increased the tension in the stadium.
Reserve goalkeeper Jose Manuel Pinto, deputising for Victor Valdes after he pulled out with a knee injury, had denied Fernando Llorente with a finger tip save, and Gorka Iraizoz pulled off a similar block from Villa.
A fabulous snaking run from Messi looked to have been halted illegally in the area, but the referee waved play on, and just when it seemed the visitors were going to deny them Xavi picked out Alves again and he crossed for Messi to score in the 77th.
"It makes me laugh when people say Barca are in crisis," Bilbao coach Joaquin Caparros told reporters. "In my view, it was the same Barca as ever."
Villarreal missed the chance to move above third-placed Valencia, who had drawn 0-0 with Sporting Gijon on Saturday, when they drew at the Madrigal.
Marco Ruben gave the hosts the lead in the 35th minute, bundling in from close range after good work from Giuseppe Rossi, but Sebastian Fernandez levelled on a counter-attack for Malaga eight minutes from time.
A third consecutive game without a win left Villarreal on 46 points, two behind Valencia. Bilbao are fifth with 38 and Espanyol sixth with 37.
Sevilla are seventh on 34 points after an Ivan Rakitic goal earned a 1-0 win over Hercules.
