The hosts, who lost 5-1 in the reverse fixture earlier in the season, must have been fearing the worst when Ivan Rakitic's brace and Alvaro Negredo's goal put the visitors on course for another memorable win just after the half-hour.
But Dorlan Pabon reduced the deficit before half-time and their cause was helped by Ruben Castro netting from the penalty spot in the 54th minute before Gary Medel was given a straight red card almost straight after.
It was not until the 90th minute that they levelled, however, Nosa Igiebor heading home to complete a memorable comeback.
In an action-packed opening few minutes, the hosts had their first sight of goal with Ruben Castro meeting Joel Campbell's cross, which forced Sevilla goalkeeper Antonio Beto to tip round the post.
It proved a key save as Rakitic gave the visitors the perfect start in the sixth minute.
Former Arsenal and Atletico Madrid winger Jose Antonio Reyes picked out the 25-year-old and he rifled low into the net from the edge of the area.
Beto was on hand to keep Sevilla's lead intact shortly afterwards after Jose Canas was given time and space to get his shot away, while at the other end, Alvaro Negredo's 20-yard piledriver was marvellously turned round the post by Betis goalkeeper Adrian.
There was nothing he could do, however, when Rakitic bagged his second of the match, Negredo laying off for the Croatia midfielder to tap in from close range in the 19th minute.
Sensing blood, Unai Emery's men continued to attack and Federico Fazio headed over from Reyes' cross.
And Betis must have feared they were on for another hiding from their rivals when Negredo put Sevilla three goals to the good in the 33rd minute.
Reyes grabbed his second assist, marauding down the left wing before picking out the Spain striker, who was left with a simple finish.
Betis gave themselves a hope of a comeback when Pabon netted two minutes before the interval, the on-loan Parma forward superbly lobbing over Beto from just inside the area.
And their hopes of mounting a memorable fightback were given a further shot in the arm when Ruben Castro slotted home from the penalty spot after Fazio was adjudged to have fouled Jorge Molina in the area in the 54th minute.
Sevilla were starting to crumble and two minutes later, their task became even harder when Medel was given a straight red card for a dangerous challenge on Jose Canas.
Unsurprisingly, the Verdiblancos immediately set about levelling proceedings although their efforts were initially repelled by a valiant Sevilla defence.
Molina fired wide of the target from a decent position although that was the closest they came to equalising as the match entered its closing stages.
But just as all seemed lost, Igiebor popped up to head high into the top corner and past a despairing Beto from Ruben Castro's right-wing cross in the 90th minute to send the home fans happy.