It was the former Atletico Madrid man’s first home game at Camp Nou after his summer switch to Catalunya for €120m (£107m/$134m) on a five-year-deal that features a release clause reported to be €800m.
Barca’s season got off to a bad start with a 1-0 defeat to Athletic Bilbao, but they roared back after falling behind to Nabil Fekir’s opener for Betis.
Griezmann scored either side of half time to draw his side level and then take the lead.
The France international World Cup winner’s brace was a historic feat as well.
Griezmann became the first person to mark his home Barcelona debut with a brace in the 21st century, quite an achievement bearing in mind the star power the Spanish champions can boast over the last 19 years.
It also ended a barren streak at Camp Nou for the ex-Real Sociedad forward.
He had not scored at the famous stadium in ten previous visits, his most times playing at a La Liga ground without finding the target.
He’ll need another goal against Betis when the sides meet in Seville later this season to mark off the arena where he’s been scoreless for the longest period now.
He’s failed to feature on the scoresheet at the Estadio Benito Villamarin in his six visits.
There was still time for Junior Firpo, signed from Betis over the summer to make his debut, the Portuguese full-back replaced Rafinha with nine minutes of the game remaining, and saw his team run out 5-2 winners.
Barcelona’s next Primera Division game sees them take on Osasuna on August 31.