Pepe Mel's side created a greater number of goalscoring opportunities than their opponents, having 19 shots compared to Granada's four, with goalkeeper Roberto Fernandez coming to the visitors' rescue on a number of occasions.
However, Granada boss Lucas Alcaraz will be ruing a chance that Youssef El Arabi missed late on that would have given them the points.
It was the hosts' second goalless draw in less than three days, following their stalemate with Lyon in the Europa League.
Mel fielded an almost entirely different team against Granada, with only Alvaro Vadillo starting both games.
Granada went into the match following a controversial 1-0 defeat to Espanyol and were again short on creativity, perhaps due to the absence of forward Francisco Medina 'Piti'.
Betis had the better of the first half, with Antonio Amaya's free-kick the closest they came to scoring, but the best chance of the first period fell to El Arabi, who failed to react quick enough to a defensive slip by Amaya in the box and headed wide.
In the second half Salva Sevilla forced Roberto into action on three occasions, the most dangerous of which was a shot from distance headed for the top corner, but the goalkeeper was able to get across and punch clear.
Fernandez also saved from Jorge Molina's close-range header, although he perhaps made the stop in a more acrobatic fashion than was necessary, as the ball was headed straight at him.
In one of Granada's few attacks, Dani Benitez sent a ball towards El Arabi at the backpost, and although Betis goalkeeper Guillermo Sara had misjudged the cross El Arabi failed to hit the target.
Cedric Mabwati had a chance to win it in the last minute, meeting a deep cross at the back post, but was unable to direct it on target, and the ball floated across the goalmouth before being cleared.
Joan Verdu then gave Roberto a fright in stoppage time, delivering a cross-shot which was inches away from creeping in at the far post.
The result means both sides are level in the table on five points.