The Primera Division side just needed a point to be sure of making it through, although Guimaraes were still in with a shout and could put pressure on should they win.
Betis did not hold back, though, and twice came close in the early stages.
Juanfran's shot from the six-yard box was tipped round the post by Ivan Vargic before Salva Sevilla shot wide from close range.
Markus Steinhofer and Manuel Jesus Chuli were wide for the hosts before Rijeka finally had an effort on goal, but Leon Benko's weak header threatened no-one.
Juan Carlos Perez Lopez curled a shot wide for Betis and Juanfran came close to putting the Spaniards ahead only for Vargic to save his effort with his feet.
Benko's header was easily taken by Betis keeper Guillermo Sara as half-time arrived with the game goalless.
Benko was the only person showing as an attacking force for the Croatians and he fired wide at the start of the second half.
The teams traded long-range efforts before Vargic was twice on hand for the visitors again, firstly to parry Steinhofer's 25-yard drive before forcing away Juanfran's shot from the centre of the area.
Andrej Kramaric had a long-range shot easily gathered by Sara as the match moved into injury time.
However, Real made it through to the next round without having been seriously threatened and some way clear after Guimaraes' defeat to Lyon.