- Tag results for Arsenal
Unai Emery's side appeared set for defeat against their newly-promoted opponents as they struggled to recover after falling behind to Ivan Cavaleiro's 13th-minute goal.
Oliver Giroud ended his 11-game goal drought this season by giving Chelsea a 53rd-minute lead, and the Premier League giants held on despite BATE striking the woodwork three times in the match.
Last season Arsenal, under Arsene Wenger, took just six points from matches against other members of the Big Six.
Emery, then in charge at Sevilla, got the better of Klopp in the final in Basel, with his side coming from behind to win 3-1, and subsequently won the French league title with Paris Saint-Germain.
Palace forward Zaha was clipped by Granit Xhaka in the closing minutes of Sunday's Premier League clash, with Luka Milivojevic converting the spot-kick to end Arsenal's 11-match winning run.
The Arsenal captain had thrown his gloves to the ground following his substitution in Sunday's 2-2 draw at Crystal Palace.
Unai Emery's side failed to win a 12th successive match in all competitions as they fell short of the club's record of 14 victories in a row.
Unai Emery's side notched their 11th win in a row on Thursday as Danny Welbeck's late strike sealed a 1-0 success at Sporting Lisbon in the Europa League.
Meanwhile, seven-time European champions AC Milan crashed to a 2-1 home defeat by Real Betis as Gennaro Gattuso's team dropped their first points in Group F.
After sealing an impressive 10th straight victory at home to Leicester in the Premier League on Monday, Unai Emery's outfit are the team to watch in Group E.
Emery's side will be pushed to the limit by the television schedulers, who moved their Premier League clash with the Foxes to Monday evening at the Emirates Stadium.
Arsenal last wore adidas' three stripes between 1986 and 1994, during which they lifted two top-flight league titles.
The former Arsenal gaffer Wenger is the longest-serving manager in the English Premier League.
The Wales international, who scored a stunning back-heel effort in Arsenal's 5-1 win at Fulham on Sunday, has scored 59 goals in 338 appearances for Arsenal since joining from Cardiff in 2008.
Lacazette and Aubameyang scored two goals each, with Aaron Ramsey netting the other one for the visitors.