Betis, who begin their own campaign in the continent's second-tier club competition at home to Olympique Lyon on Thursday, were 3-0 ahead by halftime at their Benito Villamarin stadium in Seville.
Ricardo Costa pulled a goal back with a header from Ever Banega's free kick with just over 20 minutes left but Betis comfortably thwarted Valencia's comeback bid to record their first win of the campaign.
With four matches played, Betis have four points. Valencia are stuck on three after three straight defeats following their opening day win at Malaga.
Mounir El Hamdaoui became the first player to score a hat-trick for Malaga in almost 10 years in a 5-0 success for the Qatar-owned club at home to Rayo Vallecano earlier on Sunday, their first win of the campaign.
The Morocco international, who was born in Rotterdam and has played in England, Netherlands and Italy, also made one assist on his first start for Bernd Schuster's side since joining on loan from Fiorentina in the close season.
Espanyol continued their unbeaten start with a 1-0 win at Granada and Miku grabbed a double in Getafe's 2-1 comeback win at home to struggling Osasuna.
World record signing Gareth Bale scored on his first appearance for Real Madrid on Saturday but it was a bitter-sweet debut for the 100 million euro man as Real dropped their first points of the season in a 2-2 draw at Villarreal.
Champions Barcelona and King's Cup holders Atletico Madrid are the only teams with perfect records after Barca won 3-2 at home to Sevilla and Atletico beat Almeria 4-2 at the Calderon.