The hosts came into the game in seventh place, with their opponents one point and one spot further back in the La Liga standings.
And at the end of 90 minutes that picture was unaltered, though both sides moved a point closer to sixth-placed Valencia.
The game started in a manner befitting of such a stalemate, with neither team able to create anything of substance until the 10th minute.
Getafe's Federico Fernandez was the man on the end of what was a decent chance, but he shot over from six yards.
Adrian Colunga was next to find room to shoot for the visitors, but he sent his right-footed effort wide of the post from a central position.
It took Betis 17 minutes to return fire and their first opening was also a promising one, defender Paulao heading from close-range but not finding the power to beat Jordi Codina.
Colunga worked Adrian in the Betis goal and Jorge Molina drew another save from Codina as the game opened up.
Getafe went closest to a half-time lead when Adrian made a reaction save with his feet to deny Pedro Leon.
The Betis shot-stopper continued to find himself at the centre of events in the second half, almost immediately called on to block Sergio Escudero's effort and then saving again from Colunga.
There was no shortage of shots as the European hopefuls attempted to secure maximum points, but too many efforts were off target.
When goalbound efforts were produced, the keepers were equal to them - Codina next tipping Dorlan Pabon's 20-yarder round the post.
The closing stages of the game were disrupted by substitutes and injuries and there was no late drama as the rivals settled on a share of the spoils.