Betis got off to a flying start as Santa Cruz and a Salva Sevilla penalty gave them a 2-0 lead after only 12 minutes.
Zaragoza were handed a lifeline when Betis goalkeeper Casto twice fumbled crosses to allow Efrain Juarez to prod into an empty net, but the hosts appeared to have sealed the three points within the first five minutes of the second period when Benat scored from Betis' second penalty of the evening before Santa Cruz nodded in the fourth.
Casto was then sent off for bringing down Luis Garcia just outside the box and the hosts were made to suffer with 10 men as Juan Carlos scored twice in two minutes with fine volleyed finishes at the back post but Betis held on in the final 10 minutes to make it four wins from four.
In an incredible match that flowed from end to end from the first minute it was Betis who made the early breakthrough as Javi Chica galloped behind the Zaragoza defence down the right and squared perfectly for Santa Cruz to score his first goal since joining the verdiblancos on loan from Manchester City.
Five minutes later Betis doubled their advantage when Jonathan Pereira was unnecessarily upended by Abraham just inside the area and Salva sent Roberto the wrong way from the spot.
Zaragoza responded well after that early disappointment and were worthy of their route back into the game even if it was thanks to two errors from Casto.
Firstly he flapped at a cross from the left and then failed to hold Pablo Barrera's ball back into the area allowing Juarez to stroke into an empty net.
Betis started just as brightly in the second period as they had the first and were given their second penalty when Paulo Da Silva was penalised for handling in the area, Benat this time taking responsibility to stroke home the spot-kick.
Santa Cruz then headed in his second and Betis' fourth of the evening two minutes later after another fantastic cross from Chica.
Zaragoza continued to go forward and should have had one back within a minute but Luis Garcia shanked his shot when clean through and Casto was able to scramble the ball of the line.
However, the goalkeeper was dismissed with 20 minutes to play when Garcia beat him to the ball on the edge of the area and was brought down by Casto.
The visitors made the most of their man advantage as they put the Betis defence under incessant pressure and Juan Carlos scored with a spectacular bicycle kick from Angel Lafita's cross.
Two minutes later the same player scored again with a similar volleyed finish as the Betis defence failed to clear another cross from the right.
Santa Cruz should have sealed his hat-trick as the hosts broke clear in stoppage time but headed over as Betis held on to maintain their 100% record.