Lionel Messi provided the killer pass that gave Vidal the chance to strike the 15th-minute goal that sank Valladolid, a 20th assist of the league season for the Argentinian.
Had Barcelona failed to win Saturday's game at Estadio Jose Zorrilla, Madrid would have had the opportunity at Granada to clinch the title with two games to spare. Now it cannot come until Thursday at the earliest.
Worryingly for Barcelona, they came into this game with just three wins from their last nine away games in LaLiga, but nerves were soon calmed by Vidal's fine finish.
The Chilean midfielder received a lovely dink through from Messi and quickly got away a shot low across goal, his strike going in off the left post.
Messi's assist made him the first player to reach the 20 mark in a single campaign in the Spanish top flight since Xavi in Barcelona's 2008-09 treble-winning year.
Taking into account his 22 goals this term too, Messi can hardly be blamed for Barcelona missing out on the title.
He squandered an early half-chance before missing a sitter four minutes after Barcelona's breakthrough, getting his feet in a pitiable tangle when Nelson Semedo's skidding low cross from the right reached him eight yards from goal.
Full-back Semedo had a thumping shot saved by Jordi Masip before Barcelona were thankful for Kike Perez stumbling after getting in behind their defence as the hosts sought an equalizer.
Suarez unsurprisingly replaced Griezmann for the second half, with coach Quique Setien looking for more from a Messi sidekick than the Frenchman had been able to provide.
Perez, Javi Sanchez and Enes Unal all had chances for Valladolid but could not make them count, with Marc-Andre ter Stegen kept busy, while Messi saw a free-kick tipped over by Masip, the king of the assists always a threat.