Krasnodar came from behind to draw the meeting of the two group-stage debutants.
Chelsea were held to their first 0-0 draw in more than a year.
Charles De Ketelaere got the winner deep in added time.
Lazio made an impressive return to the UEFA Champions League after 13 years away.
Álvaro Morata struck twice in the second half to secure victory.
Lionel Messi scored in this competition for a record 16th straight season as Barcelona cruised to victory despite being reduced to ten men.
Marcus Rashford struck with three minutes left to beat last season’s finalists.
Angeliño scored twice in the first 20 minutes to herald the win against the Turkish newcomers.