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.