Coton Sport of Cameroon secured a valuable away point in Group B as they drew 1-1 at Angola's Recreativo Libolo in the day's other match.
Soliman stole in unmarked at the back post to head home a 56th-minute corner and help Zamalek record a first win of this year's competition.
They move up to four points, three behind Pirates, who lead on goal difference from the other Egyptian representatives, Al Ahli.
A small but vocal crowd, who were allowed into a game that had previously been ordered to be played behind closed doors by Egyptian security officials in El Gouna, saw Zamalek win a fifth-minute penalty, successfully converted by Ahmed Eid.
But Pirates, who had won 3-0 in Egypt a month ago against holders Al Ahli, came back strongly and equalised in the 33rd minute through Lennox Bacela's deflected shot before Soliman snatched all the points for Zamalek.
In Kwanza Sul, Libolo opened the scoring from Aguinaldo's 24th-minute effort but a poor defensive clearance seven minutes later allowed Moussa Yedan to equalise for the Cameroon club.
Esperance of Tunisia top Group B on nine points, two more than Coton Sport. Libolo have four and Ivory Coast's Sewe Sport, who lost in Tunisia on Saturday, are on three.
There are two rounds left to play this month with the top two clubs in each group advancing to October's semi-finals.