The Gunners remain the only team with a perfect record in the Champions League this season, having won all five matches so far.
The result further compounded Liverpool’s recent woes, leaving Arne Slot’s team with just one win and six defeats out of their last seven league matches.
Ismaila Sarr put Crystal Palace ahead in the 41st minute.
Salah netted his 10th opening-day strike in the competition to spark wild celebrations.
Slot will become the first manager from the Netherlands to take charge of Liverpool when he resumes his new role in June.
Liverpool had initially shown interest in former player and Bayer Leverkusen manager Xabi Alonso.
