Despite Karim Benzema’s two-goal display Real ended the game having to hold on to a slender lead.
It is the first time in La Liga that a penalty kick was ordered to be re-taken after a VAR review.
Chants of 'out, out, out' rang around the Ciutat de Valencia as Griezmann was also jeered.
Lionel Messi has become Barcelona's first player to win the 10 league titles having his first title when he was 17 years old in 2005.
Atletico Madrid's 1-0 win over Real Valladolid paved the way for Barcelona to win their game over Levante.
After coming off the bench, yet again, Bale converted a controversial penalty to secure a barely deserved 2-1 league victory.
Real are 3rd in the standings on 48 points, 2 behind Atletico Madrid who beat Villarreal and still adrift of Barca, who won 4-2 at Sevilla.
Levante say Barcelona's teenage defender Chumi Brandariz was ineligible to take part in the match because he was suspended.
Griezmann has now scored all of Atletico's last six goals and this latest one, from the penalty spot, proved the difference in a cagey contest.
The Barca captain's hat-trick follows his 2 mesmeric goals from free kicks against Espanyol last week and took him on to 14 goals for the season, becoming the top scorer in La Liga and Europe's top five leagues.
Real Madrid coach Julen Lopetegui said he is not worried about the threat of being fired despite his side's loss to Levante, their third in a row.
Real Madrid coach Julen Lopetegui has now overseen a five-match winless run.
Bournemouth have signed Jefferson Lerma from Levante.
Philippe Coutinho hit a hat-trick but could not save Barcelona's unbeaten season as the Catalans were left stunned by an extraordinary 5-4 defeat to Levante on Sunday.