Enugu coach Salisu Yusuf lost his first match in charge, with the sending off of defender Temitope Olusesi not helping as they crashed 3-1 at home against Egyptian opponents Pyramids.
Two-time African champions Enyimba conceded twice within 19 minutes of the kick-off to lose 2-0 away to Moroccan outfit Hassania Agadir, who reached the quarter-finals last season.
Nigeria assistant coach Yusuf was seconded to Enugu after Benedict Ugwu lost his job for winning just once in the first five rounds of the domestic league.
Ibrahim Olawoyin put Rangers ahead on 29 minutes, but they battled after Olusesi was dismissed following a second yellow card just before half-time.
Mohamed Farouk equalised with a penalty nine minutes into the second half and Tunisian Amor Layouni and Islam Attia, from another spot-kick, scored in the closing stages for Pyramids.
The Cairo club, formerly called Al Assiouty Sport, was bought by Saudi Turki al Sheikh and he poured money into it, hiring foreign coaches and numerous Egyptian stars.
When ownership switched to Emirati Salem Al Shamsi, he spared no expense to strengthen the team with the aim of challenging traditional Egyptian giants Al Ahly and Zamalek, and seeking CAF titles.
French coach Sebastien Desabre says his targets are competing with Ahly and Zamalek for the league title and winning the Confederation Cup, the African equivalent of the Europa League.
Perfect away record
Winning in Nigeria maintained a perfect away record in the CAF competition this season by Pyramids following victories in Congo Brazzaville, Algeria and Tanzania.
The other Group A match also delivered an Egyptian victory with Karim el Eraky scoring in stoppage time to snatch a 3-2 win for Al Masry over Nouadhibou of Mauritania in Nouakchott.
A thrilling tussle saw Nigerian Austin Amutu of Masry score the only goal of the first half, then equalise after Boubacar Bagili and Yassin el Welly netted for Nouadhibou.
Pyramids and Masry have three points each, and both will enjoy home advantage in matchday two next Sunday, giving them a chance to exert an early stranglehold in the group.
In Group D, Hassania wasted no time taking control against 2003 and 2004 CAF Champions League winners Enyimba with Karim el Berkaoui and Senegalese Malick Cisse scoring.
Enyimba substitute Martins Usule blazed over when given a second-half chance during a goalmouth scramble in the southern Moroccan coastal city of Agadir.
Meanwhile, a brilliant last-minute reflex save from Moussa Camara from a Gift Motupa volley gave Horoya of Guinea a 0-0 Group C draw with Bidvest Wits of South Africa in Soweto.
In Kinshasa, Zanaco of Zambia did well to force a 1-1 draw against Daring Club Motema Pembe of the Democratic Republic of Congo after having Kelvin Kapumbu red-carded on 66 minutes.
Cameroonian Moussa Souleymanou gave the Lusaka club a 25th-minute lead that Nigerian Peter Kolawole cancelled with 12 minutes remaining.