Colombian striker Carlos Bacca was the star of a fiery contest at the Ramon Sanchez Pizjuan, scoring the opener after two minutes and creating a wonderful third for Vitolo in the second half.
But in between times Betis gave their local rivals a huge helping hand.
The sending off of key centre-back Paulao in the 42nd minute when 1-0 down for two quickfire, and needless, yellow cards made their task more difficult.
And that dismissal was compounded when Stephane Mbia headed a soft second goal immediately.
Vicente Iborra headed home the fourth in the 88th minute.
The win moved Sevilla up to eighth, but Betis remained rooted to the foot of the Primera Division table.
It was also a bad day for stuttering Valencia who were made to pay for a host of missed chances as they slumped to a 2-1 defeat at Elche, substitute Cristian Herrera netting a late winner on his league debut for the home side.
Valencia spurned a number of clear openings during a goalless first half and Elche made the most of their fortune by taking a 57th-minute lead through Fidel Chavez.
Los Che finally made one of their many opportunities count when their own substitute Juan Bernat drew them level in the 73rd minute, but it was another replacement who decided the game as Elche striker Herrera slotted home the decider six minutes from time.
The result lifts Elche on to 17 points and level with Valencia, who have now lost four of their last six Primera Division matches.
Valencia's city rivals Levante also crashed to defeat as neighbouring Villarreal continued their good start to the season with a 3-0 triumph.
The game quickly became a foregone conclusion when Levante goalkeeper Keylor Navas tripped Ikechukwu Uche in the box with just nine minutes gone and was sent off.
Bruno Soriano converted the spot-kick, and then Uche sealed the win with two second-half goals.
The victory cemented the Yellow Submarine's grip on the final Champions League spot and also marked the club's strongest ever start to a campaign in La Liga.
In Sunday's other game, Sergio Garcia hit a hat-trick as Espanyol inflicted a 4-1 defeat on 10-man Rayo Vallecano.
Like Levante, Rayo also lost their goalkeeper early on, Ruben Martinez seeing red in the 25th minute and Espanyol clinically took advantage.
Garcia netting penalties in the 28th and 51st minutes and then, moments after Saul Niguez had pulled a goal back for Rayo, completed his hat-trick in 83rd minute before Christian Stuani completed the rout.