Albian Ajeti fired the Scottish side in front and then won a penalty from which Josip Juranovic doubled the lead inside the opening half-hour.
Albian Ajeti fired the Scottish side in front and then won a penalty from which Josip Juranovic doubled the lead inside the opening half-hour of the Group G encounter at the Benito Villamarin Stadium.
Yet things began to turn sour as the Spanish side, managed by former Manchester City and West Ham boss Manuel Pellegrini, hit back to level matters with two goals in quick succession from Juan Miranda and Juanmi.
Borja Iglesias then put the hosts ahead early in the second half and Juanmi increased the advantage with his second. Anthony Ralston gave the Hoops late hope but Betis held on.
West Ham endured no such frustration as they produced an impressive display to beat Dinamo Zagreb 2-0 in Croatia.
The influential Michail Antonio opened the scoring in the 22nd minute and Declan Rice doubled the lead for David Moyes’ side five minutes into the second half.
Genk joined the Hammers level at the top of Group H after an injury-time strike from Paul Onuachu secured a 1-0 win at Rapid Vienna.
The other match in Celtic’s group, intussen, saw Bayer Leverkusen come from behind to beat Ferencvaros 2-1 with goals from Exequiel Palacios and Florian Wirtz.
Galatasaray benefited from an own goal as they opened in Group E with a 1-0 victory over Lazio in Istanbul.
Goalkeeper Thomas Strakosha got the final touch after a cross from Olimpiu Vasile Morutan was diverted towards his own goal by defender Manuel Lazzari in the 67th minute.
Substitute Tino Anjorin scored an 89th-minute equaliser as Lokomotiv Moscow snatched a 1-1 draw at home to Marseille.
In Group F, an 85th-minute penalty from Alexandar Katai gave Red Star Belgrade a 2-1 win over Sporting Braga, while Midtjylland and Ludogorets drew 1-1.