The Spanish side appeared to be the underdogs after a 1-1 draw at the Benito Villamarin last week, but they largely dominated on Thursday and put one foot in the next round when Nono scored on the stroke of half-time.
Ruben Castro then doubled their advantage on the night in the 64th minute, with Betis comfortably holding on to seal a 3-1 aggregate success.
Kazan head coach Vladimir Maminov would have had reason for cheer after his 10-men grabbed an all-important away goal last week, having looked dead and buried at 1-0 down with Alexander Prudnikov sent off for two bookable offences in as many minutes.
They started well enough at the Kazan Arena with Ruslan Mukhametshin firing over in the opening minutes.
From then on, though, it was all Betis, for whom Ruben Castro miscued one effort from the edge of the box before another was comfortably saved by Kazan goalkeeper Sergei Ryzhikov.
The 32-year-old Spanish forward continued to make a nuisance of himself but his end product was lacking, while defender Jordi Figueras drilled against the post.
Cedrick Mabwati could not finish from close range but Nono showed his team-mates how it was done with a speculative, dipping effort from 30 yards that Ryzhikov could not keep out.
The hosts then found themselves two goals down when Leo Baptistao played in Ruben Castro, who this time produced an expert finish by lobbing Ryzhikov to the delight of the away fans.
Despite boasting a two-goal advantage, Betis did not simply sit back and they almost further increased their advantage as midfielder Juanfran saw his effort from just inside the area tipped round the post.
Leo Baptistao then had his strike from a similar distance well saved by Ryzhikov, who kept the deficit down to two goals on an ultimately forgettable night for the Russian side.