Under charismatic coach Pepe Mel, Betis have made one of their best ever starts and stay three points clear of fifth-placed Andalusian rivals Malaga, who drew 1-1 at home to Celta Vigo on Saturday.
Bilbao have failed to reproduce the form that propelled them to the final of both the Europa League and the Copa del Rey last season and their night got off to the worst possible start when goalkeeper Gorka Iraizoz felled Salva Sevilla just inside the penalty area in the opening minute.
In-form Betis forward Ruben Castro stepped up and stroked his spot kick high into the net for his 12th goal of the campaign.
In an entertaining match with both teams playing attractive, attacking football, a number of chances were squandered before Ander Herrera sent Aritz Aduriz clear four minutes before half-time and he conjured a clever chip to lift the ball over onrushing Betis keeper Adrian into the net.
It was also Aduriz's 12th of the season and he and Castro are the top Spanish marksman in La Liga.
Argentine Lionel Messi of Barcelona is way out in front on 29 goals, with Real Madrid's Cristiano Ronaldo of Portugal and Colombian Radamel Falcao of Atletico Madrid both on 18.
Bilbao, who finished the match on top and almost snatched a late winner, have struggled after losing Spain international Javi Martinez to Bayern Munich in the close season and are 14th on 22 points.
Betis have 35, three behind third-placed Real Madrid, 5-0 winners at Valencia on Sunday.
"They got the penalty right after kick-off and that disrupted our plans a bit but I think the team showed it knew how to react," Aduriz told Marca TV.
"We made a big effort and I think we deserved more out of the game but the ball wouldn't go in.
"We are suffering a lot because of our position in the table and we are determined to turn things around."
Seville-based Betis, who beat champions Real 1-0 at the end of November, last took part in European competition in 2005-06 when they finished third in their Champions League group behind Liverpool and Chelsea.
They are one of many Spanish clubs to have suffered severe financial problems after years of living beyond their means and were relegated in 2008-09 before winning promotion back to the top flight two years later.
Athletic Bilbao had possession for 57.2% of the contest.
Los Rojiblancos had 16 shots, including five on target.
The five attempts by Ander were the most of any Athletic Bilbao player.
The combination of Andoni Iraola to Markel Susaeta was the most common during the match, as the two players connected 15 times.
Jon Aurtenetxe was brought on to replace Carlos Gurpegi in the 45th minute when the latter went down with an injury.