Had they dropped points for a fourth time since La Liga's restart, there would surely have been no coming back for Quique Setien's side.
But Vidal's fine finish in the 15th minute, coupled with a second-half starring role for goalkeeper Marc-Andre ter Stegen, kept pressure on leaders Real Madrid.
Until Zinedine Zidane's team cannot be caught, there will always be hope in the Barcelona ranks that Los Blancos might stumble.
"We know it depends. We just have to win all the games that we have remaining," Vidal said in a post-match interview.
"It doesn't depend on us. We just have to do what we have to do and see what the other teams around us do."
There is only one "other team" that Barcelona are concerned about, and Madrid will go to Granada on Monday hoping to capitalise on their game in hand by going four points clear with two games to play.
Barcelona have German shot-stopper Ter Stegen to thank for the fact Madrid cannot be crowned champions in that game, given that would have been the case had Setien's team dropped points in Valladolid.
Barcelona missed chances, particularly in the first half, which saw one awful fluffed effort from Antoine Griezmann, who missed his kick from in front of goal.
By the closing stages, the final whistle could not come soon enough for the flagging visiting players.
"We had our chances and didn't take them and we knew they'd have theirs," Vidal said.
"We have to improve going forward and take our chances. The important thing is we've done what we came here to do and we've got three points."
It was a hot early evening in Valladolid, and Vidal indicated Barcelona were feeling the pace in the second half.
"It's difficult against a team that were very hard to play and they played very well. Also, the conditions complicated things slightly, but I'm glad we won," he added.
"We knew we'd have to work very hard and wouldn't necessarily be able to maintain our rhythm throughout.
"We wanted to improve. We kept ourselves in the title race and that's the most important thing."