The Andalusian derby was as good as settled during a four-minute spell just after the half-hour when Betis scored three times, Ruben Castro netting the first two before Granada defender Inigo Lopez put through his own net.
Betis added a fourth goal through Dorlan Pabon at the start of the second half before Granada trimmed the deficit with a Carlos Aranda header with 18 minutes to go.
Relegation-threatened Granada could not make anymore inroads though and they were reduced to 10 men when Guilherme Siqueira was shown a second yellow card for diving, and Betis wrapped up the scoring five minutes from time with a breakaway Angel Lopez goal.
Betis gave Granada an early warning of what might be to come when in the ninth minute Colombia international Pabon drew a brilliant save out of Tono with a 25-yard effort.
Tono did well to keep that out but he was largely powerless to prevent Betis taking a stranglehold on the match midway through the first half.
Castro opened the floodgates in the 30th minute with a shot into the bottom corner and the 31-year-old doubled his account for the night 60 seconds later with a close-range tap-in after Pabon's superb chip from outside the area came down off the crossbar.
Worse was to follow for Granada as Betis added a third in the 34th minute when Lopez inadvertently bundled the ball into his own net after Junior's looping header had also come back off the bar.
Lopez thought he had made amends by pulling a goal back almost immediately, but his effort was ruled out for offside and Betis went into the break with their three-goal lead intact.
Granada made a double substitution at half-time but it barely had any time to make an impact before Betis made it 4-0, Pabon finding the back of the net in the 53rd minute from a Castro pass.
The home side finally gave their fans something to cheer in the 72nd minute when Aranda glanced home a near-post header to make it 4-1, but any hopes of an unlikely comeback ended seven minutes later when Granada lost Siqueira.
Siqueira was shown a second yellow card for simulation after going to ground inside the area.
Betis then completed a miserable night for their hosts by adding a fifth goal late on through Angel.